 # Working with Trigonometric Functions, calculus homework help Anonymous
timer Asked: Apr 25th, 2017
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vmohanakumar
School: Boston College   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 

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 

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

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  cos1 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.)

Cos1  0 

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

x = π/2.

Hence cos-1(0) = π/2

0≤x≤π

10.) Sin1 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.) Tan1 
 3 

 3
Tan1 
 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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