Question

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

Answer 1

`(4)/(5)`

Explanation:

Answer 2

sinθ = 4/5

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=√(4^2+3^2)\\\\OA=√(16+9)\\\\OA=√(25)\\\\OA=5`

Now, in triangle AOB,

`\sin\theta=(AB)/(OA)\\\\\sin\theta=(4)/(5)`

Thus, we have

sinθ = 4/5