find the value of the other trig functions if sin vada =-2/3 and cos vada is greater than 0

- Jul 4th 2008, 11:51 AMDave1234more trigonometry i dont think anyon can answer this one its to hard.
find the value of the other trig functions if sin vada =-2/3 and cos vada is greater than 0

- Jul 4th 2008, 11:59 AMJhevon
if you think no one can answer it, why did you ask? (Tongueout)

you can do this by identities, or using triangles. lets use identities here.

you should know that $\displaystyle \sin^2 \theta + \cos^2 \theta = 1$

you know the value of $\displaystyle \sin \theta$, so plug it in and solve for $\displaystyle \cos \theta$. you will get two answers, a negative one and a positive one, but they want the positive, since they said $\displaystyle \cos \theta > 0$

to do it by triangles, you can remember that sine = opposite/hypotenuse. so you can draw a right-triangle, with an acute angle $\displaystyle \theta$ with the opposite side having a length of 2 and the hypotenuse having a length of 3. then you can use Pythagoras' theorem to find the length of the adjacent side. now cosine = adjacent/hypotenuse. just plug in the values you found

By the way, it is "theta" not "vada" - Jul 4th 2008, 12:27 PMChop Suey
JHevon, you can use pythagorean identities. Or you can use the pythagorean theorem from which the identities are derived. :p

You got $\displaystyle \sin{\theta} = -\frac{2}{3}$, and hopefully you know that $\displaystyle \sin{\theta} = \frac{opposite\ side}{hypotenuse} = \frac{y}{r}$.

So, y = -2 and r = 3. Now replace in the pythagorean theorem and find x. Like JHevon said, when you take the square root of a number, you only count the positive root since you need cos(theta) > 0.

After finding x, replace:

$\displaystyle \cos{\theta} = \frac{x}{r}$