a. By considering the graphs of the functions, or otherwise, verify that: i. cos = cos

a. By considering the graphs of the functions, or otherwise, verify that:

i. cos θ = cos (−θ)

ii. sin θ = −sin (−θ)

iii. sin (θ − 90°) = −cos θ.

b. Use the results in a ii and iii to show that sin (90° − θ ) = cos θ.

c. In Example 14 you saw that cos (θ − 90°) = sin θ. Use this result with part a i to show that cos (90° − θ) = sin θ

Data from Example 14

Sketch on separate sets of axes the graphs of:

y = tan (θ + 45°), 0 ≤ θ ≤ 360° 

y = cos (θ − 90°), −360° ≤ θ ≤ 360°

Transcribed Image Text:

1 y = tan (0+ 45% 45° 35° 225° 315° 360° VE AN -360° -270° -180° -90° U y = cos (0 - 90°) [90] 90° 180° 270° 360° y = f(0 + 45°) is a translation of the graph y = f() by vector (-45°). Remember to translate any asymptotes as well. The graph of y = tan 0 is translated by 45° to the left. The asymptotes are now at 0= 45° and 0 = 225°. The curve meets the y-axis where 0 = 0 so y = 1. y = f(0-90°) is a translation of the graph y = f(0) by vector ³ (⁹09). The graph of y = cos is translated by 90° to the right. Note that this is exactly the same curve as y = sin 0, so another property is that cos (0 - 90°) = sin 0.