# Trigonometry. Sec

$\sec(\theta)=x/5$.

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

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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 en.wikipedia.org/wiki/Trigonometric_identity – Américo Tavares Apr 28 '11 at 23:45
– Isaac Apr 29 '11 at 3:49

## 1 Answer

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 $\sin$.

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@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