Question

find the exact values for sin θ cos θ and tan θ
image of a right triangle with hypotenuse 5, one leg 3, another leg 4, right angle

sin θ = □
(simplify your answer. type an integer or a fraction.)

Explanation:

Step1: Recall sine definition

In a right triangle, $\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}$.
For angle $\theta$, opposite side is 4, hypotenuse is 5.
$\sin\theta = \frac{4}{5}$

Step2: Recall cosine definition

$\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$.
Adjacent side is 3, hypotenuse is 5.
$\cos\theta = \frac{3}{5}$

Step3: Recall tangent definition

$\tan\theta = \frac{\text{opposite}}{\text{adjacent}}$.
Opposite is 4, adjacent is 3.
$\tan\theta = \frac{4}{3}$

Answer:

$\sin\theta = \frac{4}{5}$, $\cos\theta = \frac{3}{5}$, $\tan\theta = \frac{4}{3}$ (For the $\sin\theta$ part asked in the box, the answer is $\frac{4}{5}$)