Solving for Exact Trigonometric Values Using the Unit Circle 18 April 2011

Reference Angles Reference angles make it easier to find exact values of trig functions in the unit circle An angle’s distance from the x-axis

Reference Angles, cont. Always Coterminal Acute (less than ) Have one side on the x-axis

Solving for Reference Angles Step 1: Calculate the coterminal angle if necessary (Remember, coterminal angles are positive and less than 2π.) Step 2: Sketch either the given angle (if less than 2π) or the coterminal angle (if greater than 360° or 2π) Step 3: Determine the angle’s distance from the x-axis This is the reference angle!!!!

Example:

Example:

Example:

Your Turn:

Your Turn:

Your Turn:

Your Turn:

Your Turn:

Solving for Exact Trig Values Step 1: Solve for the reference angle (Note the quadrant) Step 2: Identify the correct special triangle Step 3: Identify the correct coordinates of the angle (Make sure the signs match the quadrant!) Step 5: sin t = y-coordinate; cos t = x-coordinate; Step 6: Rationalize the denominator if necessary

Example: Reference Angle: Special Triangle:

Example: Coordinates: Tangent: Sine: Cosine:

Example: Reference Angle: Special Triangle:

Example: Coordinates: Tangent: Sine: Cosine:

Example: Reference Angle: Special Triangle:

Example: Coordinates: Tangent: Sine: Cosine: