Question

score on last try: 5 of 10 pts. see details for more. at least one scored part is incorrect. jump to first changable incorrect part, jump > next question get a similar question you can retry this question below without using a calculator, compute the sine and cosine of 135° by using the reference angle. (type sqrt(2) for √2 and sqrt(3) for √3.) what is the reference angle? 45 degrees, in what quadrant is this angle? 2 (answer 1, 2, 3, or 4) sin(135°)= cos(135°)= question help: d post to forum

Explanation:

Step1: Recall sine - cosine rules for quadrant 2

In the second quadrant, $\sin\theta=\sin(180^{\circ}-\theta)$ and $\cos\theta =-\cos(180^{\circ}-\theta)$. Here $\theta = 135^{\circ}$ and its reference angle is $180 - 135=45^{\circ}$.

Step2: Find $\sin(135^{\circ})$

Since $\sin(135^{\circ})=\sin(180^{\circ}- 45^{\circ})$ and $\sin(45^{\circ})=\frac{\sqrt{2}}{2}$, then $\sin(135^{\circ})=\frac{\sqrt{2}}{2}$.

Step3: Find $\cos(135^{\circ})$

Since $\cos(135^{\circ})=-\cos(180^{\circ}-45^{\circ})$ and $\cos(45^{\circ})=\frac{\sqrt{2}}{2}$, then $\cos(135^{\circ})=-\frac{\sqrt{2}}{2}$.

Answer:

$\sin(135^{\circ})=\frac{\sqrt{2}}{2}$
$\cos(135^{\circ})=-\frac{\sqrt{2}}{2}$