How to find theta in a given trig function (pre-calc)

**deltemis** · March 29th 2009, 08:31 PM

hi guys, I need a little help with trig

the given:

if cos theta = -.25 and tan theta > 0

find the other five trig functions of theta

what I'm having problems with is how to find what theta is because I have no idea how to find the other trig functions w/o knowing the value of theta (except secant)

help would be greatly appreciated

**n0083** · March 29th 2009, 09:07 PM

$\cos(\theta) = \frac{-1}{4}$ is not a special angle so we construct a right triangle with one point at the origin, one point at (-1,0) and the hypotenuse of the triangle is 4. This is because cos = x-value/hypotenuse.

We can use pythagorean's theorem to find the other leg of this right triangle.

$4^2 = x^2 + y^2$

with x = -1

$4^2 = (-1)^2 + y^2$

$\implies y = \pm \sqrt{15}$

Your told $\tan(\theta) > 0$ , and roughly speaking tan = y-value/x-value. Because the x-value is negative we know the y-value needs to be negative to make the fraction y/x positive.

So your triangle is in the quadrant III and now you have a triangle from which to get the other trig functions.

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