Question

watch the video and then solve the problem given below. click here to watch the video. find the exact values for sin θ, cos θ, and tan θ. sin θ = (simplify your answer. type an integer or a fraction.)

Explanation:

Step1: Recall sine - cosine - tangent definitions

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, and $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Identify sides for $\sin\theta$

The side opposite to angle $\theta$ is 4 and the hypotenuse is 5. So, $\sin\theta=\frac{4}{5}$.

Step3: Identify sides for $\cos\theta$

The side adjacent to angle $\theta$ is 3 and the hypotenuse is 5. So, $\cos\theta = \frac{3}{5}$.

Step4: Identify sides for $\tan\theta$

The side opposite to angle $\theta$ is 4 and the side adjacent to angle $\theta$ is 3. So, $\tan\theta=\frac{4}{3}$.

Answer:

$\sin\theta=\frac{4}{5}$, $\cos\theta=\frac{3}{5}$, $\tan\theta=\frac{4}{3}$