# Why do I need a coterminal angle for cos(-pi/2) for the unit circle?

• Apr 15th 2009, 01:35 PM
Phire
Why do I need a coterminal angle for cos(-pi/2) for the unit circle?
According to sign rules, any negative angle given to cos is equal to the same thing with a positive sign. So essentially:

cos(-pi/2) = cos(pi/2)

In my textbook, it tells me to calculate a coterminal angle of 3pi/2 and use the unit circle. I'm not sure why I have to if pi/2 is already on the unit circle. The cos of 3pi/2 happens to be 0 also, but I have noticed that its sin value is -1, which is different than pi/2's. I want to know why the book is asking me to calculate a coterminal angle when I should be able to use pi/2? Or am I wrong?
• Apr 15th 2009, 03:38 PM
Plato
Quote:

Originally Posted by Phire
According to sign rules, any negative angle given to cos is equal to the same thing with a positive sign. So essentially: cos(-pi/2) = cos(pi/2) In my textbook, it tells me to calculate a coterminal angle of 3pi/2 and use the unit circle. I'm not sure why I have to if pi/2 is already on the unit circle. The cos of 3pi/2 happens to be 0 also, but I have noticed that its sin value is -1, which is different than pi/2's. I want to know why the book is asking me to calculate a coterminal angle when I should be able to use pi/2? Or am I wrong?

Because $\displaystyle \frac{{3\pi }}{2} + \left| {\frac{{ - \pi }}{2}} \right| = 2\pi$ means that $\displaystyle {\frac{{ - \pi }}{2}}$ is the co-terminal with $\displaystyle \frac{{3\pi }}{2}$.
• Apr 15th 2009, 05:07 PM
Phire
Quote:

Originally Posted by Plato
Because $\displaystyle \frac{{3\pi }}{2} + \left| {\frac{{ - \pi }}{2}} \right| = 2\pi$ means that $\displaystyle {\frac{{ - \pi }}{2}}$ is the co-terminal with $\displaystyle \frac{{3\pi }}{2}$.

Maybe I'm misunderstanding something, but I know that 3pi/2 is coterminal, but did I even need to find this coterminal angle to determine the cosine of -pi/2? As an experiment, I checked cos(-pi/3) and found cos(pi/3) has an equivalent value. The coterminal value of 5pi/3 is on a different spot of the unit circle but has the same cosine value. Is it because they have the same reference angle?