Evaluating Trigonometric Functions

Reference Angle 1 The measure of a reference angle is the acute angle formed by the terminal side. and the x-axis. -1 1 Initial Side Terminal Side -1

Reference Angle On the left are 3 reference angles that we know exact trig values for. To find the reference angle for angles not in the 1st quadrant (the angles at right), ignore the integer in the numerator. Then multiply the number in the numerator by the degree to find the angle’s quadrant.

Example Find the reference angle and quadrant of the following: Or 45º

Finding Exact Values of Trig Functions Find the reference angle’s value, then the quadrant to figure out the sign (+/-) R.A. Sin Cos Tan Square root # goes up 1 Reverse sine

How to Remember which Trigonometric Function is Positive 1 Just Sine (and cosecant) All S A STUDENTS ALL -1 1 TAKE CALCULUS T C Just Tangent (and cotangent) Just Cosine (and secant) -1

Example 1 Find the exact value of the following: Thought process The only thing required for a correct answer (unless the question says explain)

Example 2 Solve: Remember: There are typically 2 answers. Isolate the Trig Function What angles make the sine function 0.5? When does 4x equal our two angles? when What other angles make the sine function 0.5? Sine is cyclic, how often does it repeat?