1. C H. 4 – T RIGONOMETRIC F UNCTIONS 4.4 – Trig Functions of Any Angle

2. QUADRANT I All (sin, cos, tan) Which of the 3 major trig functions are positive? QUADRANT II Sin QUADRANT III Tan QUADRANT IV Cos All Students Take Calculus!

3. R EFERENCE ANGLES Reference angle = the acute angle formed by the terminal side of an angle and the x-axis. θ = standard angle θ' = reference angle Reference angles are always between 0° and 90° Find the reference angle for each angle below: θ = 300 ° 300 ° is in quadrant IV, so find the angle up to the positive x-axis 360° – 300° = 60° θ = -152 ° It’s in quadrant III… 180 – 152 = 28 °

4. F IND THE REFERENCE ANGLE FOR. 1. 2. 3. 4. 5.

5. F IND THE REFERENCE ANGLE FOR. 1. 2. 3. 4. 5.

6. B EYOND THE UNIT CIRCLE Ex: Find the exact values of the six trig functions of θ if the terminal side goes through the point (-5, -12). Sketch this point and see it’s in quadrant III. Make a right triangle using the reference angle Find the hypotenuse (it’ll always be positive) sin θ = -12/13 cos θ = -5/13 tan θ = 12/5 csc θ = -13/12 sec θ = -13/5 cot θ = 5/12 Don’t forget to find the hypotenuse! These points aren’t necessarily on the unit circle! (-5, -12) -12 -5 13

7. F IND THE OF AN ANGLE IN STANDARD POSITION WITH (4, 3) ON ITS TERMINAL SIDE. 1. 3/4 2. 4/5 3. 5/4 4. 4/3 5. 5/3

8. F IND THE OF AN ANGLE IN STANDARD POSITION WITH (-2, 7) ON ITS TERMINAL SIDE. 1. 2. 3. 4. 5.

9. F IND THE OF AN ANGLE IN STANDARD POSITION WITH (-4, 8) ON ITS TERMINAL SIDE. 1. 2. 3. 4. 5.