Reference Angles and Solving for Exact Trigonometric Values
Unit Circle Time! Fill out as much as you can of out the first quadrant of the unit circle from memory. Then fill in the rest from your notes when you can’t remember any more. DON’T FORGET TO PUT YOUR NAME ON THE UNIT “QUADRANT”! I’m collecting this for a classwork grade.
Solve for the reference angle for the radian measures below:
Reference Angles Matching Activity! Match each of the radian measures (in black ink) to their reference angles (in blue, red, or green ink). There will be more than one radian measure for each reference angle!!! Then indicate in which the quadrant the angle is.
Reference Angles Reference angles make it easier to find exact values of trig functions in the unit circle Measure 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 2π) Step 3: Determine the angle’s distance from the x-axis This is the reference angle!!!!
Example #7:
Example #8:
Example #9:
Your Turn:
Solving for Exact Trig Values Step 1: Solve for the coterminal angle between 0 and 2π if necessary Step 2: Solve for the reference angle (Note the quadrant) Step 3: Identify the correct coordinates of the angle (Make sure the signs of the coordinates match the quadrant!) Step 4: Solve for the correct trig ratio (Rationalize the denominator if necessary)
Example #10: Reference Angle: Coterminal Angle:
Example #10: Coordinates: Sine: Tangent: Cosine:
Example #11: Reference Angle: Coterminal Angle:
Example #11: Coordinates: Sine: Tangent: Cosine:
Example #12: Reference Angle: Coterminal Angle:
Example #12: Coordinates: Sine: Tangent: Cosine:
Your Turn: Complete problems 14 – 20.
Exit Ticket Solve for the exact values of the following:
Hmwk: Pg. 452: 31 – 47 odd