Question

chapter 5 review
score: 10/100 answered: 1/10
question 4
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°) = -1/√2
cos(135°) =
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Explanation:

Step1: Identify reference angle

The reference angle of $135^{\circ}$ is $180 - 135=45^{\circ}$.

Step2: Determine quadrant

$135^{\circ}$ is in the second quadrant. In the second quadrant, $\sin\theta> 0$ and $\cos\theta < 0$.

Step3: Recall values for $45^{\circ}$

We know that $\sin45^{\circ}=\frac{\sqrt{2}}{2}$ and $\cos45^{\circ}=\frac{\sqrt{2}}{2}$.

Step4: Find $\sin(135^{\circ})$

Since $\sin\theta$ is positive in the second - quadrant and $\sin(135^{\circ})=\sin(180 - 45^{\circ})=\sin45^{\circ}$, so $\sin(135^{\circ})=\frac{\sqrt{2}}{2}$.

Step5: Find $\cos(135^{\circ})$

Since $\cos\theta$ is negative in the second - quadrant and $\cos(135^{\circ})=-\cos(180 - 135^{\circ})=-\cos45^{\circ}$, so $\cos(135^{\circ})=-\frac{\sqrt{2}}{2}$.

Answer:

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