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

I am unsure how to answer the rest of this question, what does it mean by terminate-example-1

1 Answer

7 votes

Answer:


\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

User Chia Berry
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