Question

3. Explain USING WORDS why the answer to cos coswo colcos (1)is UNDEFINED and the answer to tan tanis3DEFINED

Answer 1

Given the expression :

$\cos (\cos ^{-1}(\frac{11}{3}))$

We should know that : the range of the cosine function is [-1 , 1]

As we can see 11/3 > 1 ,

So, the inverse cosine UNDEFINED

Which mean there is no angle have cosine 11/3

While the expression :

$\tan (\tan ^{-1}(\frac{11}{3}))$

The expression is DEFINED, because the range of tan function is all the real numbers.