# Working with Trigonometric Functions, calculus homework help

*label*Mathematics

*timer*Asked: Apr 25th, 2017

*account_balance_wallet*$25

### Question Description

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## Tutor Answer

Attached. I typed as much as I can. Let me know if you have any questions.

1.) What is the domain and range of y cos x ?

Domain: the set of all real numbers : (-∞, ∞)

Range: the set of all real numbers from -1 to 1, inclusive: [-1, 1]

2.) True or False: For a trigonometric function,

y f x

, then

x f 1 y

. Explain your answer.

False. Trigonometric functions are not one to one. Hence the inverse doesn’t exist. Inverse function

exists only for trigonometric functions with restricted domain.

3.) True or False: For a one-to-one function,

y f x

, then

x f 1 y

. Explain your answer.

True. Since the function is one to one, the inverse exists. By the definition of inverse, y = f(x), x = f-1(y).

4.) True or False: For any function,

x f 1 y

, then

y f x

. Explain your answer.

False, inverse exists only for one to one functions. All functions are not one to one.

3

,

y

sin

x

5.) True or False: The graph of

is increasing on the interval 2 2 . Explain your answer.

3

,

False. Sin(π/2) = 1, sin(π) = 0 and sin(3π/2) = -1. Therefore, the function is decreasing on 2 2

1

6.) Explain the meaning of y cos x .

y cos1 x means x = cos(y),

-1 ≤ x ≤ 1.

7.) True or False: sec 1 0.5 is undefined. Explain your answer.

1

True. 𝑠𝑒𝑐 −1 (0.5) = 𝑐𝑜𝑠 −1 ( ) = 𝑐𝑜𝑠 −1 (2), which is undefined since the domain of y = cos-1x is

0.5

[-1, 1].

8.) Find the exact value of each expression. Do not use a calculator.

9.)

Cos1 0

cos-1(0) = x, then cos(x) = 0,

x = π/2.

Hence cos-1(0) = π/2

0≤x≤π

10.) Sin1 1

Let sin-1(1) = x,

Then sin(x) = 1, -π/2 ≤ x ≤ π

x = π/2

hence sin-1(1) = π/2

3

11.) Tan1

3

3

Tan1

3

= x,

Let

Tan(x) =

𝑥 =

√3

3

−𝜋

,

2

<

𝜋

2

𝜋

6

√3

𝜋

3

6

𝐻𝑒𝑛𝑐𝑒 𝑡𝑎𝑛−1 ( ) =

Use a calculator to find the value of each expression. Round your answer to the nearest hundredth.

12.) Arcsin

...

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