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Ch. 1 - Angles and the Trigonometric Functions
Blitzer - Trigonometry 3rd Edition
Blitzer3rd EditionTrigonometryISBN: 9780137316601당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Blitzer 3rd EditionCh. 1 - Angles and the Trigonometric Functions문제 45
1장, 문제 45

In Exercises 35–60, find the reference angle for each angle.
-150°

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1
Identify the quadrant in which the angle -150° lies. Since the angle is negative, measure it clockwise from the positive x-axis. -150° corresponds to rotating 150° clockwise, which places the terminal side in the third 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 third quadrant, the reference angle is found by subtracting 180° from the angle if the angle is positive, or by subtracting the absolute value of the angle from 180° if the angle is negative.
Calculate the reference angle using the formula for negative angles in the third quadrant: Reference angle = 180° - |angle|. Substitute the given angle: Reference angle = 180° - 150°.
Simplify the expression to find the measure of the reference angle in degrees, which will be an acute angle between 0° and 90°.
Express the reference angle as a positive acute angle, which represents the smallest angle between the terminal side of the given angle and the x-axis.

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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 its acute counterpart.
추천 영상:
5:31
Reference Angles on the Unit Circle

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. Understanding this helps determine the quadrant in which the terminal side lies, which is essential for finding the correct reference angle.
추천 영상:
05:50
Drawing Angles in Standard Position

Quadrants and Angle Measures

The coordinate plane is divided into four quadrants, each corresponding to a range of angle measures. Knowing the quadrant of an angle (e.g., -150° lies in the third quadrant when converted to positive measure) helps in calculating the reference angle by subtracting from the nearest x-axis angle.
추천 영상:
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Quadratic Formula
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