# What is the value of sinθ given that (3, -7) is a point on the terminal side of θ?

-(3√58/58), 7√58/58, -(7√58/58), 3√58/58

**Solution:**

Given: (3, -7) tells us that the terminal side θ of is in the fourth quadrant

From the diagram,

We have to use the Pythagorean Theorem to find the length of the hypotenuse of the right triangle.

Let us assume the hypotenuse be h units. Then,

h^{2} = 7^{2} + 3^{2}

h^{2} = 49 + 9

h^{2} = 58

h = √58

Now we are going to use sine ratio:

sinθ = Opposite/Hypotenuse

Since, the terminal side θ of is in the fourth quadrant, the sine ratio must be negative.

So, sin θ = -7/√58

Then, rationalize the denominator we get,

sinθ = (-7/58)√58

sinθ = (-7/58)√58

Therefore, the value of sinθ is (-7/58)√58.

## What is the value of sinθ given that (3, -7) is a point on the terminal side of θ?

**Summary:**

The value of sinθ given that (3, -7) is a point on the terminal side of θ is (-7/58)√58.