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,

h² = 7² + 3²

h² = 49 + 9

h² = 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.

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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.