Finding the trig function

**goldbug78** · January 29th 2013, 08:35 AM

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?

**chiro** · January 29th 2013, 04:03 PM

Hey goldbug78.

Recall that sin^2 + cos^2 = 1 and that sin(x) >= 0 as well as cos(x) >= 0 in first quadrant.

**Soroban** · January 29th 2013, 06:03 PM

Hello, goldbug78!

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!

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