Question

What is the value of sinθ given that (−3, 4) is a point on the terminal side of θ ?

Answer 1

Answer:

sinθ = 4/5

Step-by-step explanation:

The given point is (-3,4). This point lies in the second quadrant.

In second quadrant, sinθ is positive.

Now, please see the attached image.

The point (-3,4) is at A. The hypotenuse OA can be found by using the Pythagorean theorem.

$OA=\sqrt{4^2+3^2}\\\\OA=\sqrt{16+9}\\\\OA=\sqrt{25}\\\\OA=5$

Now, in triangle AOB,

$\sin\theta=\frac{AB}{OA}\\\\\sin\theta=\frac{4}{5}$

Thus, we have

sinθ = 4/5