Sullivan Algebra and Trigonometry: Section 6.4 Trig Functions of General Angles Objectives of this Section Find the Exact Value of the Trigonometric Functions for General Angles Determine the Sign of the Trigonometric Functions of an Angle in a Given Quadrant Use Coterminal Angles to Find the Exact Value of a Trigonometric Function Find the Reference Angle of a General Angle Use the Theorem of Reference Angles

provided no denominator equals 0.

(a, b) r x y

Find the exact value of each of the six trigonometric functions of a positive angle if (-2, 3) is a point on the terminal side. (-2, 3) x y

P= (1, 0) P= (a, b) x y

P= (0,1) x y

x y (a, b) a 0 r a > 0, b > 0, r > 0 a 0, r > 0 a > 0, b 0

I (+, +) All positive x y

Two angles in standard position are said to be coterminal if they have the same terminal side. x y

Let denote a nonacute angle that lies in a quadrant. The acute angle formed by the terminal side of and either the positive x-axis or the negative x-axis is called the reference angle for Reference Angle

Finding the reference angle 2. Determine the quadrant in which the terminal side of the angle formed by the angle lies.

x y

Reference Angles

Find the exact value of each of the following trigonometric functions using reference angles: