Domanda del libro di testo
In Exercises 37–38, a point on the terminal side of angle θ is given. Find the exact value of each of the six trigonometric functions of θ, or state that the function is undefined.
(0, -1)
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Ch. 1 - Angles and the Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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Capitolo 1, Problema 37
Find the reference angle for each angle.
205°
Guida verificata passo dopo passo1
Identify the quadrant in which the angle 205° lies. Since 205° is between 180° and 270°, it is 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 \( \theta_r \) is found by subtracting 180° from the given angle: \( \theta_r = \theta - 180^\circ \).
Substitute the given angle into the formula: \( \theta_r = 205^\circ - 180^\circ \).
Simplify the expression to find the reference angle.
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Reference Angle Definition
A reference angle is the acute angle formed between the terminal side of a given angle and the nearest x-axis. It is always positive and less than or equal to 90°, used to simplify trigonometric calculations by relating angles to their acute counterparts.
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Percorso guidato
5:31
Reference Angles on the Unit Circle
Quadrants and Angle Positioning
Angles in standard position are measured from the positive x-axis counterclockwise. Knowing which quadrant an angle lies in helps determine how to calculate its reference angle, as the reference angle depends on the angle's position relative to the x-axis.
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Percorso guidato
05:50Drawing Angles in Standard Position
Calculating Reference Angles for Angles Greater than 180°
For angles between 180° and 270° (third quadrant), the reference angle is found by subtracting 180° from the given angle. This method helps convert larger angles into acute angles for easier trigonometric evaluation.
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Percorso guidato
5:31Reference Angles on the Unit Circle
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