Chapter 7: Q. 11 (page 450)

True or False $\sin (\sin^{- 1} 0) = 0 a n d \cos (\cos^{- 1} 0) = 0 .$

Short Answer

Expert verified

True statement : $\sin (\sin^{- 1} 0) = 0 a n d \cos (\cos^{- 1} 0) = 0 .$

Step by step solution

Step 1. Given Information:

Given statement:

$\sin (\sin^{- 1} 0) = 0 a n d \cos (\cos^{- 1} 0) = 0 .$

We want to know is the given statement is True or False.

Step 2. Solution:

The sin^-1 x function is the inverse function of the sin x function.

The cos^-1 x function is the inverse function of the cos x function.

Under composition of functions, the inverse function cancels the operation performed by the original function.

Therefore, the sin^-1 x function cancels the sin x and in the same context the cos^-1 x function cancels the cos x function.

This is true for $- 1 \leq x \leq 1$

We get

$\sin (\sin^{- 1} 0) = 0 \sin c e \sin a n d \sin^{- 1} c a n c e l e a c h o t h e r \cos (\cos^{- 1} 0) = 0 \sin c e \cos a n d \cos^{- 1} c a n c e l e a c h o t h e r$

Hence the statement is True.

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True or False $\sin (\sin^{- 1} 0) = 0 a n d \cos (\cos^{- 1} 0) = 0 .$

Short Answer

Step by step solution

Step 1. Given Information:

Step 2. Solution:

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True or Falsesin(sin-10)=0andcos(cos-10)=0.

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True or False $\sin (\sin^{- 1} 0) = 0 a n d \cos (\cos^{- 1} 0) = 0 .$