Summarizing Questions 1. In which quadrants is tangent positive? Why? 2. In which quadrants is cosecant negative? Why? 3. How do I sketch negative angles? 4. How can I sketch angles with multiple revolutions? 5. What are some ways of remembering the radian measures of the Unit Circle? 6. How do we get the coordinates for π/6, π/4, and π/3?
10. Sine Cosine Tangent 11. Sine Cosine Tangent
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 (It is almost always pi/denominator!!!) This is the reference angle!!!!
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:
Exit Ticket Solve for the exact values of the following: 1. 2. 3.
Summarizing Questions How do we get the coordinates for using the 45° – 45° – 90° triangle? Why are the coordinates of negative? What are the sine, cosine, and tangent of ? What is a reference angle?
Exit Ticket – “The Important Thing” On a sheet of paper (with your name!) complete the sentence below: Three important ideas/things from today’s lesson are ________, ________, and ________, but the most important thing I learned today was ________.