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?

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.

Re: Finding the trig function

Hello, goldbug78!

Quote:

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

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

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

Code:

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

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

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

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

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

Go for it!