# Finding the trig function

• Jan 29th 2013, 08:35 AM
goldbug78
Finding the trig function
Hey guys, just to make sure I am on the right track here on this question: Find the remaining trigonometric functions of θ if cos(θ) = √3/2 and θ terminates in QI. Would the sine= 1?
• Jan 29th 2013, 04:03 PM
chiro
Re: Finding the trig function
Hey goldbug78.

Recall that sin^2 + cos^2 = 1 and that sin(x) >= 0 as well as cos(x) >= 0 in first quadrant.
• Jan 29th 2013, 06:03 PM
Soroban
Re: Finding the trig function
Hello, goldbug78!

Quote:

Find the remaining trigonometric functions of $\displaystyle \theta$
if $\displaystyle \cos\theta \,=\,\frac{\sqrt{3}}{2}$ and $\displaystyle \theta$ terminates in quadrant 1.

We are given: .$\displaystyle \cos\theta \,=\,\frac{\sqrt{3}}{2} \,=\,\frac{adj}{hyp}$

Hence, $\displaystyle \theta$ is in a right triangle with: $\displaystyle adj = \sqrt{3},\:hyp = 2$
Code:

*
*  *
2  *      *
*          * x
*  θ            *
*  *  * _ *  *  *
√3

Pythagorus: .$\displaystyle x^2 + (\sqrt{3})^2 \:=\:2^2 \quad\Rightarrow\quad x^2 + 3 \:=\:4$

. . . . . . . . . . $\displaystyle x^2 \:=\:1 \quad\Rightarrow\quad x \:=\:\pm1$

Since $\displaystyle \theta$ is in quadrant 1, $\displaystyle x \,=\,+1$

You have: .$\displaystyle \begin{Bmatrix} opp &=& 1 \\ adj &=& \sqrt{3} \\ hyp &=& 2\end{Bmatrix}$

Go for it!