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

Solution:

Given:

(-3, 4) is a point on the terminal side of θ

The above point lies in the second quadrant.

In the second quadrant,

sin θ is positive.

Now, from the figure,

The point (-3, 4) is at A.

The hypotenuse OA can be found by using the Pythagorean theorem.

OA = √(4² + 3²)

OA = √(16 + 9)

OA = √(25)

OA = 5

Then, consider triangle AOB,

sinθ = AB/OA

sinθ = 4/5

Therefore, the value of sin θ is 4/5.

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

Summary:

The value of sin θ such that (-3, 4) is a point on the terminal side of θ is 4/5.