find all solutions of sin (x) = sec (x)
Answers
Sin(x)=1/cos(x)
Cos(x)•sin(x)=1
Sin(2x)/2=1
Sin(2x)=2
The solution is Option A.
The solutions of the trigonometric equation sin (x) = sec (x) is none because the range of sine is −1 ≤ y ≤ 1. Since 2 does not fall in this range, there is no solution
What are trigonometric relations?
Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the trigonometric equation be represented as A
Now , the value of A is
sin ( x ) = sec ( x ) be equation (1)
On simplifying the equation , we get
sin ( x ) = 1 / cos ( x )
Multiply by cos ( x ) on both sides of the equation , we get
sin ( x ) cos ( x ) = 1
Now , the value of the trigonometric equation sin ( 2x ) = 2sin ( x ) cos ( x )
So , Substituting the values in the equation , we get
2sin ( x ) cos ( x ) / 2 = 1
sin ( 2x ) / 2 = 1
Multiply by 2 on both sides of the equation , we get
sin ( 2x ) = 2
Now , The range of sine is −1 ≤ y ≤ 1
So , there is no solution for the equation
Hence , the solution to the trigonometric equation is none
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Related Questions
The answer to this maths question
Answers
Given:
Toilet rolls com in packs of 4 and 9.
4-pack is priced at £2.04.
9-pack is priced at £4.68.
To find:
The pack that has better value by calculating the price per roll.
Solution:
We have, the 4-pack is priced at £2.04.
So, the price per roll for this pack is:
[tex]\dfrac{2.04}{4}=0.51[/tex]
In the pack of 4 rolls the price per roll is £0.51.
It is given that, the 9-pack is priced at £4.68.
So, the price per roll for this pack is:
[tex]\dfrac{4.68}{9}=0.52[/tex]
In the pack of 9 rolls the price per roll is £0.52.
Since the price per roll in the pack of 4 rolls is less that the price per roll in the pack of 9 rolls because 0.51 < 0.52, therefore the pack of 4 rolls has better value.
Nancy is baking a cake. The recipe calls for seven cups of flour and three cups of sugar. She already put in 1/2 a cup of flour. How many more cups of flour does she need to add? Write your answer in decimal form.
Answers
Which is the graph of f(x) = 4[1/2]x ?
Answers
Step-by-step explanation:
answer is in picture see
hope it helpful
find the percent change from 4/5 to 3/5
Answers
You have a $9000 bond that earns 3% interest compounded quarterly. How much is the bond word at 6 years?
Answers
Answer:
$10,667.66
Step-by-step explanation:
The formula for calculating the compound interest is expressed as:
A = P(1+r/n)^nt
P is the principal = $9000
r is the rate = 3%
time t = 6years
n = 1/4
Substitute
A = 9000(1+0.03/(1/4))^6/4
A = 9000(1+0.03(4))^1.5
A = 9000(1+0.12)^1.5
A = 9000(1.12)^1.5
A = 9000(1.1853)
A = 10,667.67
Hence the amount after 6 years is $10,667.66
Which choice is a correct equation for the line graphed below?
Please hurry!!!
Answers
Answer:
y = 3x + 1
Step-by-step explanation:
The y - intercept is +1
And the rise over run = 3/1 (because 3 is also 3/1)
Pictures are attached.
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
A) y=3x+1
1 is the y-intercept (it is on the y axis)
you start at the 1 on the graph where the line passes through, then go 3 squares up and 1 to the right to land on the line again. This is rise over run, which you rise 3 squares up from 1, then run 1 square to the right. 3/1 = 3
Please help thanks! Brainliest
Answers
[tex]5[/tex] ✅
Step-by-step explanation:
[tex]14 + {6}^{2} \div ( - 4) \\ \\ \: = 14 + \frac{6 \times 6}{ - 4} \\ \\ \: = 14 - \frac{36}{4} \: \\ \\ = 14 - 9 \\\\ \: = 5[/tex]
Note:-
[tex]\sf\purple{BODMAS\: rule.}[/tex]
B = Brackets
O = Orders
D = Division
M = Multiplication
A = Addition
S = Subtraction
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]
Answer:
12.5
Step-by-step explanation:
14+6²÷(-4)
=14+6×6÷(-4)
=14+36÷(-4)
=50÷-4
=12.5
SUPER URGENT: Find secθ.
Answers
Answer:
B
Step-by-step explanation:
√((-20)²+21²)=√(400+441)=√841=29
cos θ=-20/29
sec θ=-29/20
At Shimla, the temperature was -14°C on Monday and then it dropped by 2°C on Tuesday. What was the temperature of Shimla on Tuesday?
Answers
Answer:
-14-2= -16
I hope it helps :)
What is the cube root of 216xy18?
O 4xy
O 6xy
O 72xBy15
O 213x®y 15
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True or False
The radius of the circle is congruent to the radius of an inscribed regular polygon inside the circle.
Answers
A polygon is a planar figure characterised by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. The given statement is True.
What is a polygon?A polygon is a planar figure characterised by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.
The given statement is true and can be observed in the given image below.
Hence, the given statement is True.
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write an equivalent logarithmic equation for e^x=24
Answers
Answer:
x=ln 24
Step-by-step explanation:
e^x=24
If we take the ln of both sides
ln e ^x= ln 24
x=ln 24
Need some assistance please
Answers
Answer:I hope this could help !ut the answer is 4
Step-by-step explanation:
2 of them left so there are 4 left
The combination locks on the lockers at Hillside School have numbers from 0 through 39 (inclusive). A locker combination consists of three different numbers, where the order matters. Because of the way the locks are manufactured, all three numbers are even or all three numbers are odd. How many combinations are possible
Answers
Answer:
13680
Step-by-step explanation:
Since we have number from 0 to 39 inclusive, there are 40 number all together.
Now there are 20 odd numbers and 20 even numbers since half of the the numbers are odd and half even.
Now, since we require 3 numbers for our locker combination which are either all even or all odd, the number of ways we can arrange 3 numbers from 20 when the order matters is ²⁰P₃ = 6480 ways for either odd or even numbers. So, for both odd and even numbers, we have the sum of even and odd number of ways ²⁰P₃ + ²⁰P₃ = 2 × ²⁰P₃ = 2 × 6480 = 13680. So, we have 13680 combinations of locks.
What’s the Missing Side?
PLEASEE HELPP
Answers
Answer:
missing side =19 ft
Step-by-step explanation:
area of a triangle =base *height/2
57=base*6/2
57*2=base*6
114=base*6
114/6=base
19 ft=base
Factor 56−16 using the GCF.
do not give me a link
Answers
F of 56 :- 2 × 2 × 2 × 7
F of 16 :- 2 × 2 × 2 × 2
HCF of 56 - 15 is 6 .
Please help asap thanks
Answers
Question 1 (1 point)
Find the probability of the pointer landing on a new house.
New Car
New House
60 120
$10,000
New Boat
Оа
1
6
Ob
1
3
Ос
60
Od
1
Ā
Answers
Answer:
[tex]P(New\ House) = \frac{1}{6}[/tex]
Step-by-step explanation:
Given
See attachment
Required
[tex]P(New\ House)[/tex]
This is calculated as:
[tex]P(New\ House) = \frac{New\ House}{Total}[/tex]
From the attachment, we have:
[tex]New\ House = 60^o[/tex]
[tex]{Total}= 360^o[/tex] --- total angle in a pie chart
Note that the measurements must be converted to degrees (if not already in degrees).
So, we have:
[tex]P(New\ House) = \frac{60}{360}[/tex]
Simplify
[tex]P(New\ House) = \frac{1}{6}[/tex]
Copy and complete the statement using < or >
-7 or -8
Answers
Answer: -7
Step-by-step explanation:
Well since where going below degrees the answer would be -7 because it is closer to 1
Will mark brainliest!
Which of the following is the result of using the remainder theorem to fin F(-2) for the polynomial function F(x)=-2x^3+x^2+4x-3?
A. -23
B. 9
C. -11
D. 3
Answers
Answer:
B
Step-by-step explanation:
To find f(- 2) substitute x = - 2 into f(x)
f(- 2) = - 2(- 2)³ + (- 2)² + 4(- 2) - 3
= - 2(- 8) + 4 - 8 - 3
= 16 + 4 - 8 - 3
= 9 → B
PLEASE HELP QUICKLY - ATTACHED BELOW MATHS
Answers
Answer:
113.081 mm²
Step-by-step explanation:
A semicircle is the half part of a circle. And we know that the semicircle have 24 mm of diameter, and the radius is 24/2 = 12 mm. The small circle is inside the semicircle, so its diameter is equal to the radius of the semicircle, and its radius is 12/2 = 6mm
Now, consider π = 3.141, the area of the small circle is:
π•6² = 3.141 • 36 = 113.076 mm²
The area of the semicircle is (π•12²)/2 = (3.141•144)/2 = 226.151 mm²
Now, you just subtract the areas:
226.151 - 113.076 = 113.081 mm²
Can you please help and I will mark brainliest if its correct
Answers
Step-by-step explanation:
diamonds and hearts are red cards
spades and clubs are black cards
15+11=26
26/52 is the probability of selecting a black card, 50%
the expanded form of 6,398 is
Answers
Answer:
The expanded form of 6,398 is 6000 + 300 + 90 + 8
Use SOH CAH TOA to identify the Tangent Z.
Answers
SOH = Sine Opposite Hypotenus
CAH = Cosine Adjacent Hypotenus
TOA = Tangent Opposite Adjacent
Based on the key I wrote above, TOA is what you will use. Starting from angle Z look at the opposite side and adjacent side. (Opposite = 21 and Adjacent = 20) Make sure you're not looking at the hypotenus which is the side that is always across from the 90° angle.
Going by opposite over adjacent, that would be 21/20
The answer is the first choice 21/20
According to a 2016 survey, 6 percent of workers arrive to work between 6:45 A.M. and 7:00 A.M. Suppose 300 workers will be selected at random from all workers in 2016. Let the random variable W represent the number of workers in the sample who arrive to work between 6:45 A.M. and 7:00 A.M. Assuming the arrival times of workers are independent, which of the following is closest to the standard deviation of W?
A. 0.24
B. 4.11
C. 4.24
D. 16.79
E. 16.92
Answers
Answer: B. 4.11
Step-by-step explanation:
Using Binomial distribution ( as the arrival times of workers are independent).
Formula for standard deviation: [tex]\sqrt{{p(1-p)}{n}}[/tex], where p= population proportion, n= sample size.
As per given ,
p= 0.06, n=300
Required standard deviation= [tex]\sqrt{0.06\left(1-0.06\right)300}[/tex]
[tex]=\sqrt{(0.06)(0.94)(300)}\\\\=\sqrt{16.92}\approx4.11[/tex]
Hence, the correct option is B.
help me pls ill give brainliest and no links pls:)!<3
Answers
As both the angles are linear, their sum is equal to 180°
i.e m<EFG+m<GFH = 180
=>( 2n+17 )+(4n+37) = 180
=> 6n + 54 = 180
=> 6n = 180-54
=>6n =126
=> n= 21
m<EFG = 2(21)+17 = 59°
m<GFH =4(21)+37 =121°
Given: ∠EFG and ∠GFH are a linear pair
We know that: Sum of the angles which make a linear pair should be equal to 180°
⇒ ∠EFG + ∠GFH = 180°
Given :
∠EFG = 2n + 17
∠GFH = 4n + 37
⇒ 2n + 17 + 4n + 37 = 180°
⇒ 6n + 54 = 180°
⇒ 6n = 180 - 54
⇒ 6n = 126
⇒ n = 21°
Substituting the value of n in ∠EFG and ∠GFH, We get:
⇒ ∠EFG = 2(21) + 17 = (42 + 17) = 59°
⇒ ∠GFH = 4(21) + 37 = (84 + 37) = 121°
PLEASE HELP QUICKLY!!! There is a tree standing in the desert; the sun is rising to the east.
Answers
b. During morning, the sun-tree-shadow changes from 180° to 90°, during noon, angle =90°.During sunset the angle changes from 90 to 0°.
c. Acute angles created in afternoon.
d. A right angle would be created at noon.
e. Obtuse angle would be created in morning.
f. Yes, a straight angle would be created at sunrise.
g. When sun is at mid-morning, the angle=45°+90°= 135°
Two similar triangles have a scale factor of 2 : 3. For numbers 7a – 7d, determine whether each statement about the triangles is true or false.
7a. The ratio of their perimeters is 2 : 3. True or False
7b. The ratio of their areas is 4 : 6. True or False
7c. Their perimeters could be 14 cm and 21 cm. True or False
7d. Two corresponding sides could be 6 in and 7 in. True or False
Answers
Answer:
Step-by-step explanation:
Two similar triangles have a scale factor of 2 : 3.
7a. The ratio of their perimeters is 2 : 3.
As the sides are 2 : 3, the perimeters which are sums of all sides will also be 2 : 3
True
7b. The ratio of their areas is 4 : 6. True or False
As the sides are 2 : 3, the areas which are the products of two sides will be in the ratio of 2*2 : 3*3 = 4 : 9
False
7c. Their perimeters could be 14 cm and 21 cm. True or False
As the perimeter ratio for 14cm and 21 cm is 14 : 21 = 2 : 3 which complies with 7a. So they could be the perimeters.
True
7d. Two corresponding sides could be 6 in and 7 in. True or False
As the corresponding sides of 6in and 7in, the ratio is 6 : 7 and is different from 2 : 3. So they cannot be corresponding sides.
False
Answer:
Step-by-step explanation:
7a. perimeter=3 sides added so the ratio is the same
The ratio of their perimeters is 2 : 3.
True
7b. area= sidexside so the ratio is 2x2:3x3 = 4:9
The ratio of their areas is 4 : 6.
False
7c. 14:21 =2:3
Their perimeters could be 14 cm and 21 cm.
True
7d. 6:7 <> 2:3
Two corresponding sides could be 6 in and 7 in.
False
Bab need someone who can do quick mafs please!
Answers
Answer:
18.9 km²
Step-by-step explanation:
Formula for area of a triangle: [tex]\frac{1}{2}bh[/tex]
0.5(7 × 5.4) = 18.9 km²
Answer:
A = 1/2 bh
1/2 x 7 x 5.4
= 18.9km2
a container of water is filled to 1/3 of it. if we add 2.5 liters the container will be half full. find how much is the volume of the container. convert it to cm³
Answers
Answer:
In picture
Step-by-step explanation:
Brainliest please
