Question

I am unsure how to answer the rest of this question, what does it mean by terminate?

Answer 1

`\tan(x) = ( -√(2) )/(4)`

Explanation:

So an angle has two parts. Initial side and terminal side.

Inital side like on x axis. and terminal side shows how much it open up. Here the terminal angle terminates in second quadrant so we have the following

• A negative Cosine Value
• A positive Sine value
• A negative Tangent Value.

Now, using Pythagoras identity let solve for cos theta.

Here you on the right track but remeber that son theta=1/3 so sin theta squared would be 1/3 squared so we have

`((1)/(3) ) {}^(2) + \cos {}^(2) (x) = 1`

`(1)/(9) + \cos {}^(2) (x) = 1`

`\cos {}^(2) (x) = (8)/(9)`

`\cos(x) = (2 √(2) )/(3)`

Note since cosine is negative in second quadrant, cos theta is

`- (2 √(2) )/(3)`

To find tan theta we do the following

`\tan(x) = ( \sin(x) )/( \cos(x) )`

`\tan(x) = ( (1)/(3) )/( (2 √(2) )/(3) )`

`\tan(x) = (1)/(2 √(2) )`

`\tan(x) = (2 √(2) )/(8)`

`( √(2) )/(4)`

So

`\tan(x) = ( -√(2) )/(4)`

Tan is negative in second quadrant