Question

The length of which line segment is equal to the exact value of the sine if theta?

Option 3: line segment OR
Option 4: line segment OS​

Answer 1

Answer: Option 2. Segment TS

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Step-by-step explanation:

Recall that the sine of an angle is equal to the ratio of opposite over hypotenuse.

In other words,

sin(angle) = opposite/hypotenuse

With respect to reference angle theta, the side TS is opposite this angle. It is the leg furthest from the angle. The hypotenuse is the longest side segment TO. The hypotenuse is always opposite the 90 degree angle.

For a unit circle, the radius is 1, so segment TO is 1 unit long.

Therefore,

sin(angle) = opposite/hypotenuse

sin(theta) = TS/TO

sin(theta) = TS/1

sin(theta) = TS