Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have a homework problem that I don't know what to do with. We were just introduced to sum and difference identities. We've always been provided values in degrees both in class and in homework until this problem. I checked the book to see if a similar problem had been worked out; it hadn't. Any help would be appreciated.

Use the information below to find the exact value of sin (A-B): $\cos A = \dfrac1{3}, 0 < A < \dfrac{\pi}{2}, \sin B = -\dfrac1{2}, \dfrac{3\pi}{2} < B < 2\pi$

share|cite|improve this question
up vote 1 down vote accepted

Hint: You should have $\sin (A-B)= \sin A \cos B - \cos A \sin B$ and $\sin^2 \theta + \cos^2 \theta = 1$. To find $\sin A$, we use the second:

$\sin^2 A + \cos^2 A=1$

$\sin^2 A = \frac 89$

$\sin A = \pm \frac {2 \sqrt 2}3$

The restriction on $A$ should let you resolve the $\pm$ sign. Now do the same to find $\cos B$ and you have all you need for the first equation.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.