1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
enot [183]
3 years ago
15

Given that tan θ ≈ −0.087, where 3 2 π < θ < 2 , π find the values of sin θ and cos θ.

Mathematics
1 answer:
elena-s [515]3 years ago
4 0

Answer:

  • sin θ ≈ -0.08667
  • cos θ ≈ 0.99624

Step-by-step explanation:

Straightforward use of the inverse tangent function of a calculator will tell you θ ≈ -0.08678 radians. This is an angle in the 4th quadrant, where your restriction on θ places it. (To comply with the restriction, you would need to consider the angle value to be 2π-0.08678 radians. The trig values for this angle are the same as the trig values for -0.08678 radians.)

Likewise, straightforward use of the calculator to find the other function values gives ...

  sin(-0.08678 radians) ≈ -0.08667

  cos(-0.08678 radians) ≈ 0.99624

_____

<em>Note on inverse tangent</em>

Depending on the mode setting of your calculator, the arctan or tan⁻¹ function may give you a value in degrees, not radians. That doesn't matter for this problem. sin(arctan(-0.087)) is the same whether the angle is degrees or radians, as long as you don't change the mode in the middle of the computation.

We have shown radians in the above answer because the restriction on the angle is written in terms of radians.

_____

<em>Alternate solution</em>

The relationship between tan and sin and cos in the 4th quadrant is ...

  \cos{\theta}=\dfrac{1}{\sqrt{1+\tan^2{\theta}}}\\\\\sin{\theta}=\dfrac{\tan{\theta}}{\sqrt{1+\tan^2{\theta}}}

That is, the cosine is positive, and the sign of the sine matches that of the tangent.

This more complicated computation gives the same result as above.

You might be interested in
The bear lake is 24 miles long. Suppose John starts cycling art one end at 20 m.p.h. and Ramona starts at the other end at 15 m.
Fed [463]

Answer:

24/35 hours  or 0.69 hours

Step-by-step explanation:

we know that

The speed is equal to divide the distance by the time

Let

x-----> distance traveled by John

(24-x) ----> distance traveled by Ramona

The time is equal to divide the distance by the speed

so

x/20=(24-x)/15

15x=20(24-x)

15x=480-20x

15x+20x=480

35x=480

x=480/35 miles

the time is equal to

t=x/20

t=480/(20*35)=24/35=0.69 hours

8 0
3 years ago
I need help I’m timed<br> what is the y- intercept of the linear function? <br> y= 1/2 x + 4
Gennadij [26K]

Answer: (0,4)

Step-by-step explanation:

5 0
3 years ago
Based on the information below what are the values of x and y of the solution to the system of equations used to create the info
Grace [21]

Answer:

<em>(D). x = 2 , y = - 5</em>

Step-by-step explanation:

A = - 8 + 48 = 40

A_{x} = -76 + 156 = 80

A_{y} = 104 - 304 = - 200

<em>x =</em> \frac{A_{x} }{A} = <em>2</em>

<em>y =</em> \frac{A_{y} }{A} = <em>- 5</em>

<u><em>( 2, - 5 )</em></u>

3 0
2 years ago
Read 2 more answers
Evaluate the following expression 5^-2/5^0
Ray Of Light [21]

Answer:

Step-by-step explanation:

1/25

4 0
3 years ago
Two poles, A and B, are 12 meters apart. Pole A is 5 meters high. A rope 20 meters long is tied to the top of pole A and stretch
stepan [7]
The answer should be C, 21. I’ll attach a picture for explanation.
5 0
3 years ago
Other questions:
  • What is the exact answer is betwwen 6×7,381
    5·2 answers
  • Harriet and Richard go shopping and by 66 items altogether. Harriet buys twice as many items as Richard. How many items does Har
    6·2 answers
  • What is repeating 8.333 in fration form as mixed and improper form?
    6·1 answer
  • What is the approximate area of a regular pentagon with a side length of 6 feet and a distance from the center to a vertex of 6
    13·2 answers
  • Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in s
    10·1 answer
  • 2.4(5.5r -2.5) = 17.1<br> Round answer to nearest 10th
    10·1 answer
  • How do you do this and what ya the correct answer? Simple and concise explanation please!
    7·1 answer
  • Identify all the sets to which the number belongs. Choose from rational number, irrational number, whole number, an integer.
    7·1 answer
  • Identify the terms, coefficients, and constants in the expression.<br> 8x+7y^2
    5·1 answer
  • Help for this question
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!