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Chapter 4: Problem 105

If you are given a point on the terminal side of angle \(\theta\) explain how to find \(\sin \theta\)

Short Answer

Expert verified
The sine of an angle in the unit circle is the y-coordinate of the point on the terminal side of the angle. You simply look at the y-value of the given point to find \(\sin \theta\).

Step by step solution

01

Understand the Unit Circle

A unit circle is a circle with a radius of 1, centered at the origin (0,0) on a coordinate plane. Any point \(P\) on the circle can be represented as \((x, y)\) where \(x\) is the horizontal coordinate and \(y\) is vertical. The angle \(\theta\) is measured from the positive x-axis to the line segment OP in counter-clockwise direction.
02

Definition of Sine

In the unit circle, \(\sin \theta\) of an angle \(\theta\) is defined as the y-coordinate of a point on the terminal side of the angle. This comes from the definition of sine in right triangles, and is expanded to apply to all angles using the unit circle.
03

Calculate Sine

To find \(\sin \theta\), we simply look at the y-coordinate of the given point on the terminal side of \(\theta\).

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