Answers
Hi there!
To find the Trigonometric Equation, we have to isolate sin, cos, tan, etc. We are also given the interval [0,2π).
First Question
What we have to do is to isolate cos first.
[tex] \displaystyle \large{ cos \theta = - \frac{1}{2} }[/tex]
Then find the reference angle. As we know cos(π/3) equals 1/2. Therefore π/3 is our reference angle.
Since we know that cos is negative in Q2 and Q3. We will be using π + (ref. angle) for Q3. and π - (ref. angle) for Q2.
Find Q2
[tex] \displaystyle \large{ \pi - \frac{ \pi}{3} = \frac{3 \pi}{3} - \frac{ \pi}{3} } \\ \displaystyle \large \boxed{ \frac{2 \pi}{3} }[/tex]
Find Q3
[tex] \displaystyle \large{ \pi + \frac{ \pi}{3} = \frac{3 \pi}{3} + \frac{ \pi}{3} } \\ \displaystyle \large \boxed{ \frac{4 \pi}{3} }[/tex]
Both values are apart of the interval. Hence,
[tex] \displaystyle \large \boxed{ \theta = \frac{2 \pi}{3} , \frac{4 \pi}{3} }[/tex]
Second Question
Isolate sin(4 theta).
[tex] \displaystyle \large{sin 4 \theta = - \frac{1}{ \sqrt{2} } }[/tex]
Rationalize the denominator.
[tex] \displaystyle \large{sin4 \theta = - \frac{ \sqrt{2} }{2} }[/tex]
The problem here is 4 beside theta. What we are going to do is to expand the interval.
[tex] \displaystyle \large{0 \leqslant \theta < 2 \pi}[/tex]
Multiply whole by 4.
[tex] \displaystyle \large{0 \times 4 \leqslant \theta \times 4 < 2 \pi \times 4} \\ \displaystyle \large \boxed{0 \leqslant 4 \theta < 8 \pi}[/tex]
Then find the reference angle.
We know that sin(π/4) = √2/2. Hence π/4 is our reference angle.
sin is negative in Q3 and Q4. We use π + (ref. angle) for Q3 and 2π - (ref. angle for Q4.)
Find Q3
[tex] \displaystyle \large{ \pi + \frac{ \pi}{4} = \frac{ 4 \pi}{4} + \frac{ \pi}{4} } \\ \displaystyle \large \boxed{ \frac{5 \pi}{4} }[/tex]
Find Q4
[tex] \displaystyle \large{2 \pi - \frac{ \pi}{4} = \frac{8 \pi}{4} - \frac{ \pi}{4} } \\ \displaystyle \large \boxed{ \frac{7 \pi}{4} }[/tex]
Both values are in [0,2π). However, we exceed our interval to < 8π.
We will be using these following:-
[tex] \displaystyle \large{ \theta + 2 \pi k = \theta \: \: \: \: \: \sf{(k \: \: is \: \: integer)}}[/tex]
Hence:-
For Q3
[tex] \displaystyle \large{ \frac{5 \pi}{4} + 2 \pi = \frac{13 \pi}{4} } \\ \displaystyle \large{ \frac{5 \pi}{4} + 4\pi = \frac{21 \pi}{4} } \\ \displaystyle \large{ \frac{5 \pi}{4} + 6\pi = \frac{29 \pi}{4} }[/tex]
We cannot use any further k-values (or k cannot be 4 or higher) because it'd be +8π and not in the interval.
For Q4
[tex] \displaystyle \large{ \frac{ 7 \pi}{4} + 2 \pi = \frac{15 \pi}{4} } \\ \displaystyle \large{ \frac{ 7 \pi}{4} + 4 \pi = \frac{23\pi}{4} } \\ \displaystyle \large{ \frac{ 7 \pi}{4} + 6 \pi = \frac{31 \pi}{4} }[/tex]
Therefore:-
[tex] \displaystyle \large{4 \theta = \frac{5 \pi}{4} , \frac{7 \pi}{4} , \frac{13\pi}{4} , \frac{21\pi}{4} , \frac{29\pi}{4}, \frac{15 \pi}{4} , \frac{23\pi}{4} , \frac{31\pi}{4} }[/tex]
Then we divide all these values by 4.
[tex] \displaystyle \large \boxed{\theta = \frac{5 \pi}{16} , \frac{7 \pi}{16} , \frac{13\pi}{16} , \frac{21\pi}{16} , \frac{29\pi}{16}, \frac{15 \pi}{16} , \frac{23\pi}{16} , \frac{31\pi}{16} }[/tex]
Let me know if you have any questions!
Related Questions
find the product using suitable product 854×102 step by step explanation
Answers
Answer:
87108
Step-by-step explanation:
854 x 102
= 854 x ( 100 + 2 )
= 854 ( 100 ) + 854 ( 2 )
= 85400 + 1708
= 87108
854
102 x
——-
87108
What is the remainder of 119 divided by 4
Answers
Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.
The remainder when dividing 119 by 4 is 3.
We have,
To find the remainder when dividing 119 by 4, we perform the division and observe the remainder.
When we divide 119 by 4, we get:
119 ÷ 4 = 29 remainder 3
The quotient is 29, which means that 4 goes into 119 twenty-nine times without any remainder.
However, there is a remainder of 3.
Therefore,
The remainder when dividing 119 by 4 is 3.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ6
solve for "X" where x±4=12
Answers
Answer:
x = 8, 16
Step-by-step explanation:
x + 4 = 12
x = 12- 4
x = 8
x - 4 = 12
x = 12 + 4
x = 16
A tennis coach divides her 9-player squad into three 3-player groups with each player in only one group. How many different sets of three groups can be made?
Answers
Answer:
84
9 choose 3
Step-by-step explanation:
Is the relationship shown by the data linear? If so, model the data with an equation.
Answers
Ravi bought 50kg rice at the rate of tk.40 per kg and sold it at the rate of tk.44 per kg. What is the percentage of profit
Answers
He paid 0.40 x 50 = 20
He sold it for 0.44 x 50 = 22
His profit was 22-20 = 2
Percentage was 2/20 = 0.10 = 10 %
Answer 10 %
Look at the numbers below. −9.8 −5.4 1.0 14.8 Which shows the best way to add these numbers using the Commutative and Associative Properties? A. (–9.8 + 1.0) + (–5.4 + 14.8) B. (–9.8 + 14.8) + (–5.4 + 1.0) C. (1.0 + 14.8) + (–9.8 + (–5.4)) D. (1.0 + (–9.8)) + (14.8 + (–5.4)
Answers
Answer:
B
Step-by-step explanation:
i did the test and it was correct, ur welcome
when A = 300, solve the equation
[tex] {x }^{2} - 40x + a = 0[/tex]
Answers
Answer:
Solution given:
a=300
and equation is:
x²-40x+a=0
when a=300
x²-40x+300=0
making it a perfect square
x²-2*20x+20²-20²+300=0
(x+20)²-400+300=0
(x+20)²=100
x+20=±10
taking positive
x+20=10
x=10-20
x=-10
taking negative
x+20=-10
x=-10-20
z=-30
when A=300
x=-10 or -30
Write the equation of the line for the graph shown below.
Answers
Answer:
The answer is C
Step-by-step explanation:
y=-5x-3
Hope this helped
Answer:
I believe the answer is y = -5x -3
Step-by-step explanation:
The formula is y=mx+b
m= rise over run
b= starting point
and seeing how the dot is on -3 I assume that the answer is y= -5x -3
also m should be in fraction form and if it isn't, you automatically put a 1 as the denominator.
Find the value of x on this triangle
Answers
Answer:
33
a2+b2 =c2
a2+ 33 squared = 55 squared
a + 1936 = 3025
3025-1936=1089
square root of 1089 is 33
pleeeaaasssseeee mark as brainliest
!HELP PLEASEEE! For this problem I thought it meant to subtract 0.1492 - 0.1515 = -0.0023 however my answer was incorrect. How do I solve this problem then? Help Please!
Answers
?????????????????????
Answers
Answer:
[tex]g(x)=x+6[/tex]
Step-by-step explanation:
The problem gives one the following information:
[tex]h(x)=(f\ \ o\ \ g)(x)\\\\h(x)=\sqrt[4]{x+7}\\f(x)=\sqrt[4]{x+1}[/tex]
This problem now requires one to find the function ([tex]g(x)[/tex]).
The format:
[tex](f\ \ o\ \ g)(x)[/tex]
Is another way of writing a composition of a function. In essence, it indicates this operation:
[tex](f(g(x))[/tex]
This means that one has to input one function into another. In other words, substitute one function into another in place of the variable, then simplify and solve to find the new function that is derived from this operation. Since it is given that ([tex]h(x)[/tex]) is the function resulting from the composition of ([tex]f(g(x))[/tex]), an equation can be formed. Treat the evaluator ([tex]g(x)[/tex]) as another variable. Then simplify and solve the equation to find the function that represents ([tex]g(x)[/tex]).
[tex]h(x)=f(g(x))[/tex]
Substitute,
[tex]h(x)=f(g(x))[/tex]
[tex]\sqrt[4]{x+7}=\sqrt[4]{(g(x)+1}[/tex]
Since both numbers are equivalent to each other when one takes the quartic root of the numbers, the numbers underneath the radical must be equivalent to each other. Therefore, one can state the following:
[tex]\sqrt[4]{x+7}=\sqrt[4]{(g(x)+1}[/tex]
[tex]x+7=(g(x))+1[/tex]
Inverse operations:
[tex]x+7=(g(x))+1[/tex]
[tex]x+7-1=g(x)\\[/tex]
[tex]x+6=g(x)[/tex]
Chứng minh hệ thức De Morgan sau:
~(P ^ Q) = ~P v ~Q
Answers
Use a truth table:
p … q … p ∧ q … ¬(p ∧ q) … ¬p … ¬q … ¬p ∨ ¬q
T … T … T … F … F … F … F
T … F … F … T … F … T … T
F … T … F … T … T … F … T
F … F … F … T … T … T … T
Singh's house the weekly consumption of milk is 6.5 liters what is their daily consumption of milk if they consume same quantity of milk every day
Answers
Answer:
Their daily consumption of milk is of 0.93 liters.
Step-by-step explanation:
Weekly consumption:
6.5 liters.
Daily consumption:
A week has 7 days.
Each day the amount consumed is the same, so the daily consumption is:
6.5/7 = 0.93
Their daily consumption of milk is of 0.93 liters.
Zane wants to enlarge two of his photos to frame on his bedroom wall. He has 184 photos from rock concerts he's been to and 88 photos of city
skylines
How many possible combinations of 1 rock concert photo and 1 city skyline photo could Zane choose from?
Answers
Answer:
B
Step-by-step explanation:
184*88=16,192
in a small town in New York, we initiated a cohort study and followed 5,900 people for a mean follow-up of 2 years. At the end of the 2nd year, none of the participants was lost to follow-up. During this follow-up, we identified 600 cases of malaria. What was the cumulative incidence?
a. 10.1%
b. 10.1 per 1,000
c. 50.8%
d. 10 cases
Answers
Answer:
Option A
Step-by-step explanation:
From the question we are told that:
Sample size n=5900
Number of newly developed cases No.C=600
Generally the equation for Cumulative Incidence is mathematically given by
[tex]CI=\frac{No.C}{n}[/tex]
[tex]CI=\frac{600}{5900}[/tex]
[tex]CI=0.101[/tex]
[tex]CI= 10.1%[/tex]
Option A
Which sets of ordered pairs show equivalent ratios? Use the grid to help you.
Check all that apply.
A: (1, 2), (2, 3), (4, 7)
B: (2, 2), (4, 4), (6, 6)
C: (3, 1), (4, 1), (5, 1)
D: (4, 1), (8, 2), (12, 3)
E: (2, 1), (4, 3), (5, 4)
Answers
Answer:
B and D
Step-by-step explanation:
in B the ratio of x/y = 1 for all pairs.
in D the ratio of x/y = 4 for all pairs.
in all other sets there are different ratios inside the set.
Answer:
The pairs (2, 2), (4, 4), and (6, 6) have ratios of 1 and the pairs (4, 1), (4, 1), (8, 2), and (12, 3) have ratios of 4. The other pairs do not have similar ratios.
Step-by-step explanation:
Step 1; In order to pair up the pairs with equivalent rations, we first need to calculate the ratios for all the pairs by dividing the first value with the second value. The same procedure must be followed throughout to be able to pair them up.
Step 2; By dividing the values, the ratios are;
For (1, 2), the ratio is = 0.5,
For (2, 3), the ratio is = 0.6666,
For (4, 7), the ratio is = 0.5714,
For (2, 2), the ratio is = 1,
For (4, 4), the ratio is = 1,
For (6, 6), the ratio is = 1,
For (3, 1), the ratio is = 3,
For (4, 1), the ratio is = 4,
For (5, 1), the ratio is = 5,
For (4, 1), the ratio is = 4,
For (8, 2), the ratio is = 4,
For (12, 3), the ratio is = 4,
For (2, 1), the ratio is = 2,
For (4, 3), the ratio is = 1.333,
For (5, 4), the ratio is = 1.25.
Step 3; Now we pair up the sets with the same ratios, out of these 15 pairs. The pairs (2, 2), (4, 4), and (6, 6) have ratios of 1 and the pairs (4, 1), (4, 1), (8, 2), and (12, 3) have ratios of 4. The other pairs do not have similar ratios.
I hope this is right and it helps you !!!!!!!!!!
Does the graph below represent a proportional relationship?
———————————————
A. Yes, because the graph is a straight line
B. No, because it crosses the y -axis
C. Yes, because it crosses the y -axis
D. No, because the line doesn't pass through the origin, point (0,0)
Answers
The reason being straight lines mean equal proportions, while curved lines are exponential or quadratic.
Answer: D. No, because the line doesn't pass through the origin, point (0,0)
Explanation:
A direct proportional graph is always a straight line through the origin.
Algebraically, the form of any direct proportion equation is y = kx, where k is some constant. It plays the role as the slope.
We can rewrite y = kx as y = kx+0 to see that the y intercept is always 0 for these types of equations.
Unfortunately, this line shown has a y intercept of 2 instead of 0. So it's not a direct proportion.
8 and 1/3divided by 3 and 4/7
Answers
7/3
Step-by-step explanation:
8 1/3 divided by 3 4/7
Let’s start by 8 1/3
Multiply 3 x 8 and then add 1
3 x 8 = 24 + 1 = 25
Add the denominator back
25/3
3 4/7
Multiply 7 x 3 and then add 4
7 x 3 = 21 + 4 = 25
Add the denominator back
25/7
Final Results: 25/3 & 25/7
Now we’re ready to divide!
Multiply 7 by 25
7 x 25 = 175
Multiply 3 by 25
3 x 25 = 75
Answer: 175/75
Finally Simplify
175/75 = 7/3
Final Answer: 7/3
A baseball is projected upward at 64 feet per second. It can be approximated by the equation -16t^2+64t. The baseball reaches it maximum height at the vertex. That can be gotten from x= −/2a . How long until the baseball reaches its full height? Note a quadratic equation can be written as ax^2+bx+c
Answers
Answer:
f(t) = -16t²+64t
t = number of secondsf(t) = height (in feet)The x-coordinate(t) of the vertex can be found using formula [tex]\frac{-b}{2a}[/tex], where:
a = -16b = 64Therefore the t-value of the vertex is:
[tex]\frac{-64}{2(-16)} =\frac{-64}{-32} =2[/tex]
The baseball will reach its maximum height after two seconds.
HELP THIS IS DUE BY THURSDAY PLZZ HELP ME (05.03)Bev has to cut her grandma's grass this weekend and wants to know exactly how much area she will be cutting. Calculate the area of the polygon. Be sure to show all your work and explain your answer
Answers
Answer: 220.5 ft^2
That's the answer.
What is the least possible degree of a polynomial that has the root -3 + 2i, and repeated root -2 that occurs twice?
4
3
2
5
Answers
Answer:
4
Step-by-step explanation:
complex roots always occur in pairs.
so roots are -3+2i,-3-2i ,-2,-2
number of roots=4
The price of a car was decreased from $13,000 to $11,830. The price is decreased by what percentage?
Answers
Answer:
It is decreased by 9%
Step-by-step explanation:
First, find out how much money is decreased. To do this, subtract 13,000-11,830=1170. Finally, figure out how much percent 1170 is of the original price of $13,000.
The answer is 7%.
Hope this helps :)
WILL MARK BRAINLIEST
Which is a recursive formula for this geometric sequence?
- 3, 6, - 12, 24, ...
Answers
Answer:
Step-by-step explanation:
B
PLEASE HELP! much appreciated :D
Find the value of x.
Answers
Answer:
a
Step-by-step explanation:
Which expression is equivalent to 7x , if b > 0?
Answers
Work Shown:
[tex]7x^2*\sqrt{2x^4}*6\sqrt{2x^{12}}\\\\7*6x^2*\sqrt{2x^4*2x^{12}}\\\\42x^2*\sqrt{4x^{4+12}}\\\\42x^2*\sqrt{4x^{16}}\\\\42x^2*\sqrt{(2x^8)^2}\\\\42x^2*(2x^8)\\\\42*2x^{2+8}\\\\84x^{10}\\\\[/tex]
So that's why the answer is choice C
The requirement that x is nonzero isn't technically necessary. The original expression simplifies to choice C even when x = 0 is the case. Also, we don't have issues such as division by zero errors that could arise. It's a bit curious why your teacher put in that condition.
Answer:
C.
Step-by-step explanation:
7x²×sqrt(2x⁴)×6×sqrt(2x¹²)
we see right away that as constant multiplication factor we have 7×6 = 42.
and then we get from each sqrt expression a sqrt(2), which leads to sqrt²(2) = 2 and therefore 42×2=84.
the only answer option with 84 is C.
now, to be completely sure, and to get some practice, let's look at the other parts :
sqrt(2x⁴) = sqrt(2)×sqrt(x⁴) = sqrt(2)×x²
sqrt(2x¹²) = sqrt(2)×sqrt(x¹²) = sqrt(2)×x⁶
=>
7x²×sqrt(2)×x²×6×sqrt(2)×x⁶ =7×6×2×x²×x²×x⁶ = 84x¹⁰
perfect. C is confirmed.
In a volcano, erupting lava flows continuously through a tube system about 15 kilometers to the sea. Assume a lava flow speed of 0.5 kilometer per hour and calculate how long it takes to reach the sea.
Answers
9514 1404 393
Answer:
30 hours
Step-by-step explanation:
The relation between time, speed, and distance is ...
time = distance/speed
time = (15 km)/(0.5 km/h) = 30 h
It takes 30 hours for the lava to reach the sea.
simplify 4x + 3y - 2x
Answers
Answer:
2x+3y
Step-by-step explanation:
4x + 3y - 2x
Combine like terms
4x-2x +3y
2x +3y
Like terms
4x-2x which equals 2x
So
2x+3y
Proving the Single Opposite Side Pair Theorem
Given: AD = BC and AD || BC
Prove: ABCD is a parallelogram.
Angles Segments Triangles Statements Reasons
ZBCA
ZDAC
А
Statements
Reasons
B
D
с
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Answers
9514 1404 393
Explanation:
1. AD ≅ BC, AD ║ BC . . . . given
2. ∠DAC ≅ ∠BCA . . . . alternate interior angles theorem
3. AC ≅AC . . . . reflexive property
4. ΔDAC ≅ ΔBCA . . . . SAS postulate
5. AB ≅ CD, ∠BAC ≅ ∠DCA . . . . CPCTC
6. AB ║ CD . . . . converse of alternate interior angles theorem
7. ABCD is a parallelogram . . . . definition of a parallelogram (has 2 pairs of parallel & congruent sides)
_____
We don't know what your tiles/choices are for statements or reasons. We have shown the triangles are congruent, so their corresponding parts (sides/angles) are congruent. That lets us claim opposite sides are congruent and parallel. YMMV
Answer:
Picture Down Below
Step-by-step explanation:
Ophelia is making homemade spaghetti sauce by combining 48 oz of tomato paste with 6 cups of water.how many cups of water are needed for every ounces of tooth paste
Answers
1 cup per 8 oz
48/6 = 8
every 1 cup of water 8 oz of tomato paste.
explained : there are 48 oz of tomato paste and 6 cups of water 48 over 6 is 8 therefore per every 1 cup of water there are 8 oz of tomato paste
