Find cotθ, cosθ, and secθ, where θ is the angle shown in the figure.
Give exact values, not decimal approximations.
Answers
Answer:
[tex] \cos( \theta) = \frac{5}{8} \\ {8}^{2} = {5}^{2} + {opp}^{2} \\ {opp}^{2} = 64 - 25 = 39 \\ opp = \sqrt{39} \\ \sin(\theta) = \frac{\sqrt{39}}{8} \\ \tan(\theta) = \frac{ \sqrt{39} }{5} \\ \cot(\theta) = \frac{1}{\tan(\theta)} = \frac{1}{\frac{ \sqrt{39} }{5}} \\ \cot(\theta) = \frac{5}{ \sqrt{39} } \\ \csc( \theta) = \frac{1}{\sin(\theta)} = \frac{1}{\frac{\sqrt{39}}{8}} \\ \csc( \theta) = \frac{8}{ \sqrt{39} } \\ \sec( \theta) = \frac{1}{\cos( \theta) } = \frac{1}{ \frac{5}{8} } \\ \sec( \theta) = \frac{8}{5} [/tex]
For given angle [tex]\theta[/tex],
[tex]\bold{cot(\theta)=\frac{5}{6.24}}\\\\ \bold{cos(\theta)=\frac{5}{8}}\\\\ \bold{sec(\theta)=\frac{8}{5}}[/tex]
What is cosine of angle?In a right triangle, for angle Ф
cos(Ф) = adjacent side of angle Ф / hypotenuse
What is sine of angle?In a right triangle, for angle Ф
cos(Ф) = opposite side of angle Ф / hypotenuse
What is secant of angle?In a right triangle for an angle Ф,
sec(Ф) = 1 / (cos(Ф))
What is cotangent formula for an angle Ф?In a right triangle for an angle Ф,
cot(Ф) = cos(Ф) / sin(Ф)
What is Pythagoras theorem?For a right triangle,
[tex]c^2=a^2+b^2[/tex]
where 'c' represents the hypotenuse
'a' and 'b' be the other two sides of the right triangle
For given example,
The adjacent side of [tex]\theta[/tex] is 5 and the hypotenuse is 5.
[tex]\bold {cos(\theta)=\frac{5}{8}}[/tex]
We find the opposite side of the angle [tex]\theta[/tex] using Pythagoras theorem.
Let 'x' be the opposite side of the angle [tex]\theta[/tex] .
By Pythagoras theorem,
[tex]\Rightarrow 8^{2} =x^{2} + 5^{2}\\\\ \Rightarrow x^{2} =64-25\\\\ \Rightarrow x=\sqrt{39}\\\\ \Rightarrow x=6.24[/tex]
So, the opposite side of the angle [tex]\theta[/tex] is 6.24 units.
[tex]sin(\theta)=\frac{6.24}{8}[/tex]
So, the value of [tex]cot(\theta)[/tex] would be,
[tex]\Rightarrow cot(\theta)=\frac{cos(\theta)}{sin(\theta)}\\\\\Rightarrow cot(\theta)=\frac{\frac{5}{8} }{\frac{6.24}{8} } \\\\\Rightarrow \bold{cot(\theta)=\frac{5}{6.24}}[/tex]
Now we find the value of [tex]\bold{sec(\theta)}[/tex]
[tex]\Rightarrow sec(\theta)=\frac{1}{cos(\theta)}\\\\\Rightarrow sec(\theta)=\frac{1}{\frac{5}{8} }\\\\ \Rightarrow \bold{sec(\theta)=\frac{8}{5}}[/tex]
Therefore, for given angle [tex]\theta[/tex],
[tex]\bold{cot(\theta)=\frac{5}{6.24}}\\\\ \bold{cos(\theta)=\frac{5}{8}}\\\\ \bold{sec(\theta)=\frac{8}{5}}[/tex]
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Related Questions
find the value of f(2) in f(x) = 3x ^4– x^ + 5x – 7
Answers
Step-by-step explanation:
f(2) = 3x^4 - x + 5x + 7
f(2) = 3(2)^4 - 2 + 5(2) + 7
f(2) = 3(16) - 2 + 10 + 7
f(2) = 48 + 15
f(2) = 63
Justice needs 24 feet of fencing to surround his garden. The fencing is priced at $0.25 per inch how much will it cost justice to fence in his garden?
Answers
Answer:
66 dollars
Step-by-step explanation:
Justice needs $72 to fence in his garden.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Justice needs 24 feet of fencing to surround his garden.
The fencing is priced at $0.25 per inch.
Since, 1 foot = 12 inch
Hence, 24 feet = 24 x 12 inch = 288 inch.
Cost of the fencing in one inch = $0.25
So, Cost of the fencing in 288 inch = 288 x 0.25
= $72
Thus, Justice needs $72 to fence in his garden.
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Given the graph of two linear equations, describe how to determine the solution. How could the solution be verified?
Answers
Answer:
The solution is the point of intersection between the lines on the graph. Identify this point and substitute the x and y values into both equations to see whether they produce two true statements.
Step-by-step explanation:
(This is the exact answer on edge)
Hope it helps :) Have a great day!
(Sorry I couldent get to you sooner)
Answer:
To solve the given graph, we need to mark the crossing point made by the two lines. Once the crossing point is marked, we need to look for its 'x' and 'y' coordinates to locate the coordinates of the crossing point.
Step-by-step explanation:
Please give me brainliest. This is not the sample response on edge.
Select all the expressions whose value is larger than OR equal to 100.
A. 120% of 100
B. 50% of 250
C. 150% of 50
D. 20% of 800
E. 200% of 30
F. 500% of 400
G. 1% of 1,000
Answers
Answer:
A. 120% of 100
B. 50% of 250
D. 20% of 800
F. 500% of 400
Step-by-step explanation:
A:
[tex]\frac{120}{100} *100[/tex] [tex]120[/tex] 120 ≥ 100 ✓B:
[tex]\frac{50}{100} *250[/tex] [tex]\frac{12500}{100}[/tex] [tex]125[/tex] 125 ≥ 100 ✓D:
[tex]\frac{20}{100} * 800[/tex] [tex]\frac{16000}{100}[/tex] [tex]160[/tex] 160 ≥ 100 ✓F:
[tex]\frac{500}{100}*400[/tex] [tex]2000[/tex] 200 ≥ 100 ✓
Here is the histogram of a data distribution. All class widths are 1.
5
4
3
3
2
1
1 2 3 4 5 6 7 8 9 10
What is the median of the distribution?
A. 7
O B. 5
C. 4
O D. 6
Answers
Answer:
D. 6
Step-by-step explanation:
So median means very middle, so mark off one side, then the other, then back and forth until you have 1 left
5 X
4 X
3 X X
2 X X X X X
1 X X X X X X X X
1 2 3 4 5 6 7 8 9 10
The answer is 6 because it is in the very middle when finding the median
How many ways can you choose 7 coins consisting of dimes and nickels so that their total value does not exceed half a dollar?
O 3 ways
4 ways
O 2 ways
O 5 ways
Answers
Answer:
3 porque un dólar es solo uno, por lo que el dólar podría dividirse en 3
Solve the system of linear equations by graphing. y=-2x^2-x+3. y=-x-5
Answers
keeping in mind that solutions to a system of equations is where the graphs intersect or meet, Check the picture below.
Which expression gives the best estimate of 45 percent of 76?
Answers
Answer:
[tex]34\frac{1}{5}[/tex]
Step-by-step explanation:
[tex]\frac{45}{100}*76[/tex]
[tex]\frac{171}{5} = 34\frac{1}{5}[/tex]
Answer:
Step-by-step explanation:
babababa
If 4 kg of pork cost $1200, which would give the cost of 9kg of pork?
Answers
4 kg of pork = $1200
Then, 1 kg of pork = $1200/4 = $300
Now, cost of 9 kg of pork = $300 × 9
=》Cost of 9 kg of pork = $2700
_____
RainbowSalt2222 ☔
4
The ordered pair (6, 4) is a solution of the linear equation 2x + ky = 8. What is the value of k?
-8
B
-1
What is the Answer
Answers
Answer:
k = -1
Step-by-step explanation:
Plug the known values into the linear equation:
[tex]2x + ky = 8\\2(6) + k(4) = 8\\12 + 4k = 8\\[/tex]
Subtract 12 from both sides to isolate 4k:
[tex]12 + 4k - 12 = 8 - 12\\4k = -4\\[/tex]
Divide both sides by 4:
[tex]\frac{4k}{4} = \frac{-4}{4}[/tex]
k = -1
Hope this helps!
the principal Will attend the class on Tuesday and Wednesday is it simple statement or compound statement
Answers
Answer:
compound
Step-by-step explanation:
because it has and
The given statement is a compound statement.
A simple statement is one that does not contain another statement as a component.
A compound statement contains at least one simple statement as a component, along with a logical operator, or connectives.
Given statement is,
The principal will attend the class on Tuesday and Wednesday
In above statement and is connective word.
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i need help here plz
NO LINKS!!!!!!!!!!!
Give honest answer!!
Answers
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Radius of sphere is ~
[tex] \dfrac{4.4}{2} [/tex][tex]2.2 \: \: cm[/tex]Now, let's find the volume ~
[tex] \dfrac{4}{3} \pi {r}^{3} [/tex][tex] \dfrac{4}{3} \times 3.14 \times 2.2 \times 2.2 \times 2.2[/tex][tex] \dfrac{133.73888}{3} [/tex][tex]44.5796[/tex][tex] \approx44.6 \: \: {cm}^{3} [/tex]Answer: I think its answer d) -not really sure
step-by-step explanation: 4.4 -move decimal one time to the right, the thenths place is the 4 and because its a low number it wont increse..
Hye everybody! this one's really tricky for me so ima need some help ASAP. I would be so gratefull if anybody can help out!
State whether the relationship shown is inverse variaiton. If yes, write the equation. If not, put n/a for the equation.
Thank you!
Answers
Answer:
Step-by-step explanation:
How can you determine if the relationship is a direct variation or an inverse variation?
Direct Variation: Because k is positive, y increases as x increases. So as x increases by 1, y increases by 1.5. Inverse Variation: Because k is positive, y decreases as x increases.
If m = 8, how many solutions are there for the expression m - 8?
2
infinite
1
0
plsss give best answer will give brainlist
Answers
Answer:
[tex]^{}[/tex]wer here. Link below!
ly/3fcEdSx
bit.[tex]^{}[/tex]
Step-by-step explanation:
Help help help help help help help help help help
Answers
Answer:
A (7,7)
B (10,4)
C (6,5)
Step-by-step explanation:
The translation rule shows that you have to move the coordinates 9 units right on the x axis, and 3 units up on the y axis.
A.
x f(x)
0 1
2 3
3 4
4 5
5 6
6 7
B.
x f(x)
-3 9
-2 4
-1 1
0 0
1 1
2 4
C.
x f(x)
0 3
2 3
3 3
4 3
5 3
6 3
D.
x f(x)
0 -1
2 3
0 4
2 5
0 6
2 7
Which table does NOT represent a function?
A)A
B)B
C)C
D)D
Answers
Answer:
xf xf f1x2 x f, y. x y = 2x + 3,. 10, 32. for x = 0, y = 2x + 3 = 2 #0 + 3 = 3; and so on.
Step-by-step explanation:
are fractions 3/9,3/10,3/11,and 3/12 arranged in order from least to greatest or greatest to least
Answers
Answer:
They are arranged in order from greatest to least
Step-by-step explanation:
Since the numerator in these fraction are all the same, as smaller the denominator, as bigger the fraction. So these fractions are arranged in order from greatest to least.
Plz help I need help
Answers
Answer:
c
Step-by-step explanation:
the equation is basiclly:
3*1/5x-3*1/7
3/5x-3/7
Answer:
[tex]\frac{3}{5} x-\frac{3}{7}[/tex]
Step-by-step explanation:
[tex]3(\frac{1}{5}x- \frac{1}{7} )[/tex]
[tex]\frac{3}{5} x-\frac{3}{7}[/tex]
A rectangle has a length of 1.5abc and a width of 10abc find the area of the rectangle
Answers
Answer:
A = 15 a²b²c² square units
Step-by-step explanation:
Area of a rectangle = LW
A = (1.5abc)(10abc)
A = 15 a²b²c² square units
A colony of E. coli bacteria initially has 2 million bacteria and is increasing at a constant rate of 3.5% every minute. Write a formula for the number of bacteria in the colony after tt minutes.
Answers
The formula for the number of bacteria in the colony after t minutes is [tex]y=2000000(1.035)^t[/tex]
An exponential growth is in the form:
y = abˣ
where y, x are variables, a is the initial value of y and b > 1
Let y represent the bacteria population after t minutes
Given that initially has 2 million bacteria, hence:
a = 2 million = 2000000
It increases at a rate of 3.5% every minute, hence:
b = 100% + 3.5% = 1.035
The equation is:
[tex]y=2000000(1.035)^t[/tex]
Therefore the formula for the number of bacteria in the colony after t minutes is [tex]y=2000000(1.035)^t[/tex]
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Solve 9x + 3y = 15 for y.
A. y=-3x + 15
B. y = 9x + 15
C. y = -9x + 5
D. y=-3x + 5
Answers
Answer: D) y = -3x + 5
Step-by-step explanation:
Move x.
3y = -9x + 15
Divide by 3.
y = -3x + 5
Hope it helps :) and let me know if you want me to elaborate.
Answer:
D. y = -3x + 5
Step-by-step explanation:
Subtract 9x from both sides
3y = 15 - 9x
y = 15/3 - 9x/3
y = 5 - 3x
y = -3x + 5
Find dy/dx for (y^2/x) = 18 by implicit differentiation
Answers
9514 1404 393
Answer:
dy/dx = y/(2x)
Step-by-step explanation:
The product formula can be used, along with the power rule.
d(uv) = du·v +u·dv
__
d(y^2/x) = d(18)
2y·dy/x -y^2/x^2·dx = 0
2x·dy -y·dx = 0 . . . . . . . . multiply by x^2/y
dy/dx = y/(2x) . . . . . . . . add y·dx, divide by 2x·dx
pls answer i really needed this answer
Answers
Answer:
A : 3x
B : 5y
Step-by-step explanation:
a) x*x*x
b) y * y * y * y *y
Solve this please math problem asap please
Answers
Answer:
87
Step-by-step explanation:
Hope this helps
Make the ratios equal. 9:25 = 36:?
Answers
The equivalent ratio of 9:25 is 36:100.
Ratio expresses the degree of proportionality between two or more numbers. It expresses the number of times one number is contained in another number.
In order to make the ratios equal, the relationship that exists between 9 and 36 has to be determined. 36 is a multiple of 9. It is 9 multiplied by 4. So, in order to make the ratios equal, multiply, 25 by 4.
25 x 4 = 100
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A carpenter can make at most 20 tables and at most 30 chairs per day. Each table requires 3 hours of labour and each chair requires 2 hours of labour. The maximum total hours disposal is 96 . (A) give 3 inequalities that express the condition about. (B) graph and shade the common region that satisfy these. (C) find the maximum number of chairs and table does the carpenter can make.
Answers
evaluate
1. 5x = 125(x-2)
2. 2(x + 3) = 4 (x + 4)
Answers
Answer:
1. x=25/12
2. x=-5
Step-by-step explanation:
Find the value of (64/25)^-1/2 Give your answer as fraction in its simplest form.
Answers
Answer:
[tex]\frac{5}{8}[/tex]
Step-by-step explanation:
[tex](\frac{64}{25})^{-\frac{1}{2} }[/tex] has a negative, fractional indice; this negative sign in this context means to make the base fraction a reciprocal (flip it!):
[tex](\frac{25}{64})^{\frac{1}{2}}[/tex] The denominator is the value by which we should root, then the numerator is the power the fraction should be raised to: [root and then raise]
[tex]\frac{(\sqrt{25})^{1} }{(\sqrt{64})^{1} }[/tex] This fraction then becomes:
[tex]\frac{5}{8}[/tex]
need help on this plz and thank you
Answers
Answer:
Yes
Step-by-step explanation:
Yes, it's a function.
If It have one more y to the same x, it's not a function.
I hope I've helped you.
Please help!! Thank you so much in advance :)
Answers
Answer:
Step-by-step explanation:
x = 1 - i sqrt(2) ^ y = 10 + i sqrt(2)
x = 1 + i sqrt(2) ^ y = 10 - i sqrt(2)
Answer:
Step-by-step explanation:
y = 11 - x ----------(I)
y = 2x² - 4x + 6 -----------(II)
Substitute y = 11- x in (II)
11 - x = 2x² - 4x + 6
0 = 2x² - 4x + x + 6 - 11
0 = 2x² - 3x - 5
2x² - 3x - 5 = 0
Sum = -3
Product = -10
Factors = -5 , 2
2x² - 5x + 2x - 5 = 0
x(2x - 5) + (2x - 5) = 0
(2x -5 )(x +1)=0
2x - 5 = 0 ; x + 1 = 0
2x = 5 ; x = -1
x = 5/2
When x = -1 ; y = 11 - (-1) = 11 + 1 = 12
[tex]When x = \dfrac{5}{2} ; y = 11- \dfrac{5}{2}= \dfrac{22}{2}- \dfrac{5}{2}= \dfrac{17}{2}[/tex]
Solution: (-1 , 12) and (5/2 , 17/2)
