Question

express the trig ratios as fractions in simplest terms.
answer attempt 1 out of 8
sin i =
cos h =
sin i and cos h

Explanation:

Step1: Recall sine definition

$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$
For $\angle I$, opposite side is $GH=33$, hypotenuse is $HI=55$.
$\sin I = \frac{33}{55}$

Step2: Simplify $\sin I$

Divide numerator/denominator by 11:
$\sin I = \frac{33\div11}{55\div11} = \frac{3}{5}$

Step3: Recall cosine definition

$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$
For $\angle H$, adjacent side is $GH=33$, hypotenuse is $HI=55$.
$\cos H = \frac{33}{55}$

Step4: Simplify $\cos H$

Divide numerator/denominator by 11:
$\cos H = \frac{33\div11}{55\div11} = \frac{3}{5}$

Step5: Compare the two values

Since $\sin I = \frac{3}{5}$ and $\cos H = \frac{3}{5}$, they are equal.

Answer:

$\sin I = \frac{3}{5}$, $\cos H = \frac{3}{5}$, $\sin I$ and $\cos H$ are equal