2. Aim: How do we find the exact values of trig functions? Do Now: Evaluate the following trig ratios a) sin 45  b) sin 60  c) sin 135  HW: p.380 # 34,36,38,42 p.391 # 8,12,14,16,24,26

3. y x O 1 Draw 135  on the standard position Form a triangle in quadrant II. B We will use the ΔAOB to find the trig ratios for angle 135  A The triangle is an isosceles right triangle and  AOB is 45  How do we proceed?

4. First of all, we need to find the reference angle. Reference angle: An acute angle that is formed by the x-axis and the terminal side of an angle in standard position. If which is in the quadrant II, therefore, the reference angle is formed by and the negative x- axis. Then the reference angle is 45  y x 1 Use the triangle in quadrant II, we can find the trig ratios of  135  Reference angle 45  Principal angle

5. y x Reference angle 45  in quadrant III y x Reference angle 45  in quadrant IV y x If the angle is in quadrant I, then the principal angle and reference angle are the same

6. The rules to find the reference angle for any angle within 360  Quadrant I: Principal angle & reference angle are the same Quadrant II: angle is (180  – θ) Quadrant III: angle is (θ – 180  ) Quadrant IV: angle is Where θ represents principal angle (180  – θ)

7. Based on the rules, 30 , 150 , 210  and 330  all have the same reference angle. 30  : the reference angle is still 30  in quadrant I 150  : the reference angle is 180 – 150 = 30  in quadrant II 210  : the reference angle is 210 – 180 = 30  in quadrant III 330  : the reference angle is 360 – 330 = 30  in quadrant IV

8. To find the trig ratios for any angle from 0 to 360, we first find the reference angle then use the rules of ASTC to determine the signs. Find the value of a) sin 225  b) cos 315  225  is in quadrant III and the reference angle is 45  sin 225 is just like sin 45 in quad III 315  is in quadrant IV and the reference angle is 45  cos 315 is just like cos 45 in quad IV

9. Find the exact values of the following trig functions a)sin 240 b)sin 225 c) cos 135 d) sin -330

10. e) cos 120 f) cos 225 g) cos 315 h) cos -60

11. i) sin 420 j) tan 315 k)tan 210 l)tan -120