Home > A2C > Chapter 10 > Lesson 10.2.4 > Problem10-110

10-110.

If $\operatorname { tan } \theta = \frac { 1 } { 2 }$ and $\pi \leq \theta \leq \frac { 3 \pi } { 2 }$, what is the value of $\operatorname{sin}θ$?

$\text{Remember that} \operatorname{tan}\theta=\frac{\text{opp}}{\text{adj}}.$

Use the Pythagorean theorem to find the hypotenuse.

$\left(\text{hyp}\right)^{2} = \left(2\right)^{2} + \left(1\right)^{2}$

$\text{hyp}=\sqrt{5}$

Be careful, $θ$ is in the third quadrant, so sine is negative.

$\operatorname{sin }\theta=\frac{\text{opp}}{\text{hyp}}$