Question

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express the trig ratios as fractions in simplest terms.
answer attempt 1 out of 2
sin q = □
cos p = □
sin q and cos p
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Explanation:

Step1: Recall sine definition for $\angle Q$

For right triangle, $\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$
For $\angle Q$, opposite side = $PO = 2$, hypotenuse = $QP = 3$
$\sin Q = \frac{2}{3}$

Step2: Recall cosine definition for $\angle P$

For right triangle, $\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$
For $\angle P$, adjacent side = $PO = 2$, hypotenuse = $QP = 3$
$\cos P = \frac{2}{3}$

Step3: Compare the two values

Since $\sin Q = \frac{2}{3}$ and $\cos P = \frac{2}{3}$, they are equal.

Answer:

$\sin Q = \frac{2}{3}$, $\cos P = \frac{2}{3}$
$\sin Q$ and $\cos P$ are equal