In Exercises 35–60, find the reference angle for each angle.
355°

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Identify the quadrant in which the angle 355° lies. Since 355° is between 270° and 360°, it is in the fourth quadrant.

Recall that the reference angle is the acute angle formed between the terminal side of the given angle and the x-axis.

For angles in the fourth quadrant, the reference angle \( \theta_{ref} \) is calculated by subtracting the angle from 360°: \( \theta_{ref} = 360^\circ - \theta \).

Substitute the given angle into the formula: \( \theta_{ref} = 360^\circ - 355^\circ \).

Simplify the expression to find the reference angle.

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주요 개념

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Reference Angle

A reference angle is the acute angle formed between the terminal side of a given angle and the x-axis. It is always positive and less than or equal to 90°, used to simplify trigonometric calculations by relating any angle to an acute angle.

Standard Position of an Angle

An angle in standard position has its vertex at the origin and its initial side along the positive x-axis. The terminal side rotates counterclockwise for positive angles and clockwise for negative angles, determining the angle's quadrant and reference angle.

Quadrants and Angle Measurement

The coordinate plane is divided into four quadrants, each spanning 90°. Knowing the quadrant of an angle helps find its reference angle by subtracting or adding the angle to the nearest x-axis boundary (0°, 90°, 180°, 270°, or 360°).

In Exercises 35–60, find the reference angle for each angle.355°