Help on unit circle problems

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Introduction for practice unit circle problems:

Trigonometry is the study of angles and the physical relationships between angles and geometry. To start, we use the unit circle, which is a circle of radius 1 unit, centered at the origin. The trigonometric functions are defined using unit circle. The unit circle is nothing but circle of radius equal to one unit. Angles can be measured in 2 ways, in degrees or in radians. Practice unit circle problems would be useful for us to understand the concepts of trigonometric unit circle concepts. Let us see the practice unit circle problems.

In the given figure, find the exact coordinates of the intersection of the unit circle and the terminal side of the

angle.

The coordinates of the point at which the terminal side of the angle with measure θ intersects the unit circle are

x = cos θ

y = sin θ

Substitute 45 for θ

x = cos 45 = 1/(√ 2)

y = sin 45 = 1/(√ 2).

The coordinates of the point are:

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