Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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


What does $\sin(\theta)$ equal? What does $\tan(\theta)$ equal?

share|cite|improve this question
Draw out a representative right triangle with theta as one of the acute angles. What proportion of sides is the secant function? Can you find the value of all the sides? And from there, can you find sine and tangent? – Michael Chen Apr 28 '11 at 23:32
Look at "List of trigonometric identities, Trigonometric functions" in Wikipedia – Américo Tavares Apr 28 '11 at 23:45

As Michael Chen has alluded to:

Start by noting that

$$\sec \theta = \frac{1}{\cos \theta} = \frac{x}{5}$$

so that $$\cos \theta = \frac{5}{x}$$

Now you know that $\cos \theta$ is the 'adjacent / hypotenuse ' of a right angled triangle. So...draw the triangle, and work out what the unknown side ('opposite') will be, and then use the definition of $\tan$ and $\sin$.

share|cite|improve this answer
@sara: To "work out... the unknown side", use the Pythagorean Theorem with x as the length of the hyponetuse. – The Chaz 2.0 Apr 29 '11 at 4:58

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.