1 / 10

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

Aim: How do we find the exact values of trig functions?. Do Now: Find the following trig functions. sin 45 . b) sin 60 . c) sin 135 . HW: p.372 # 14,16 p.380 # 34,36,38,42 p.391 # 8,12,14,16,24,26. y. Draw 135  on the standard position. A. 1. O.

bud
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Aim: How do we find the exact values of trig functions? Do Now: Find the following trig functions • sin 45 b) sin 60 c) sin 135 HW:p.372 # 14,16 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: angle is the same Quadrant II: angle is (180–θ) Quadrant III: angle is (θ– 180) Quadrant IV: angle is

  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 us 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

More Related