Question

I need to know how to 53 evaluate the inverse trigonometric function give answers in both radians and degrees

Answer 1

GIVEN:

We are given the following trigonometric expression;

`Tan^(-1)(-1)`

Required;

We are required to evaluate and answer both in radians and in degrees.

Step-by-step solution;

We shall begin by using the trig property;

`tan^(-1)(-x)=-tan^(-1)(x)`

Therefore, we now have;

`tan^(-1)(-1)=-tan^(-1)(1)`

We now use the table of common values and we'll have;

`tan^(-1)(1)=(\pi)/(4)`

Therefore;

`-tan^(-1)(1)=-(\pi)/(4)`

We can now convert this to degrees;

`\begin{gathered} Convert\text{ }radians\text{ }to\text{ }degrees: \\ (r)/(\pi)=(d)/(180) \end{gathered}`

Substitute for r (radian measure):

`\begin{gathered} (-(\pi)/(4))/(\pi)=(d)/(180) \\ \\ -(\pi)/(4)/(\pi)/(1)=(d)/(180) \\ \\ -(\pi)/(4)*(1)/(\pi)=(d)/(180) \\ \\ -(1)/(4)=(d)/(180) \end{gathered}`

Now we can cross multiply;

`\begin{gathered} -(180)/(4)=d \\ \\ -45=d \end{gathered}`

Therefore,

ANSWER:

`\begin{gathered} radians=-(\pi)/(4) \\ \\ degrees=-45\degree \end{gathered}`