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Aim: How do we find the exact values of trig functions?

Aim: How do we find the exact values of trig functions?. Do Now: Evaluate the following trig ratios. sin 45 . b) sin 60 . c) sin 135 . HW: p.380 # 34,36,38,42 p.391 # 8,12,14,16,24,26. y. Draw 135  on the standard position. A. 1. O.

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Aim: How do we find the exact values of trig functions?

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

  2. y Draw 135 on the standard position A 1 O Form a triangle in quadrant II. B -1 x The triangle is an isosceles right triangle and AOB is45 We will use the ΔAOB to find the trig ratios for angle 135 How do we proceed?

  3. 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 Principal angle y Use the triangle in quadrant II, we can find the trig ratios of 135 1 x -1 Reference angle 45

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

  5. 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 (180 – θ) Where θ represents principal angle

  6. 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

  7. 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

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

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

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

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