Give the degree measure of θ. Do not use a calculator.
θ = arcsin (―√3/2)

Verified step by step guidance

1. Understand that \( \theta = \arcsin(-\sqrt{3}/2) \) means we are looking for an angle whose sine is \(-\sqrt{3}/2\).
2. Recall that the sine function is negative in the third and fourth quadrants.
3. Identify the reference angle where \( \sin(\theta) = \sqrt{3}/2 \) is \( 60^\circ \) or \( \pi/3 \) radians.
4. Determine the angles in the third and fourth quadrants that have a reference angle of \( 60^\circ \).
5. Conclude that the possible angles are \( 240^\circ \) and \( 300^\circ \) in degrees.

Key Concepts

Inverse Trigonometric Functions

Inverse trigonometric functions, such as arcsin, are used to find the angle whose sine is a given value. For example, if θ = arcsin(x), then sin(θ) = x. Understanding how to interpret these functions is crucial for solving problems involving angles and their corresponding trigonometric ratios.

Unit Circle

The unit circle is a fundamental concept in trigonometry that defines the relationship between angles and their sine, cosine, and tangent values. It is a circle with a radius of one centered at the origin of a coordinate plane. Knowing the coordinates of key angles on the unit circle helps in determining the sine and cosine values for those angles, which is essential for solving arcsin problems.

Reference Angles

Reference angles are the acute angles formed by the terminal side of an angle and the x-axis. They are used to simplify the process of finding trigonometric values for angles in different quadrants. For example, when finding arcsin(―√3/2), recognizing that the sine value corresponds to a specific reference angle can help determine the correct angle θ in the appropriate quadrant.