A central angle, t, of a unit circle has the terminal side in the fourth quadrant and has a cosine of x. What is the cosine of t+pi/2?

Question

A central angle, t, of a unit circle has the terminal side in the fourth quadrant and has a cosine of x. What is the cosine of t+pi/2?

 

A. x/2

B. –x

 

C. x

D. 2x

Answer 1

Hi Mae.  This is a very interesting problem.  It sounds like the terminal side can be *anywhere* in quadrant IV.  Your best bet to getting the correct answer is really by eliminating impossible choices.  So here it goes:

 

Choice B.  -x

When the terminal side is in IV the x value (or cosine) is always GTE zero.  When we rotate the angle by pi/2 (90 degrees) the terminal side is in quad I, where the x value/cosine  is still GTE zero.  So -x is not possible.

 

Choices D and A seem *possible* without putting too much effort into it.  But...

 

Choice C is definitely possible.  In fact, cos(7*pi/4) = cos(pi/4) = √2/2.

 

So if the question states that you must choose one and only one answer, C would be the choice.