MCR3U Worksheet – Trigonometric Equations & CAS

MCR3U Worksheet – Trigonometric Equations & CAST Rule Date: ______________

Trig Identities worksheet 3.3 name: Prove each identity:

1. cscθ =

cotθ cosθ

2.

1 sec2 x

+ 1

csc2 x = 1

3. csc 2 y tan2 y − 1 = tan2 y 4.

secθ cosθ

− tanθ cotθ

= 1

5. csc 4 x − cot4 x = csc2 x + cot2 x 6. sec

4 y − tan4 y = tan2 y + sec2 y

7. 1 − tanθ( )2 = sec2 θ − 2tanθ 8.

1 − sin2 x( ) 1 + tan2 x( ) = 1

Trig Identities worksheet 3.3

9.

cotw cosw

+ sec w cot w

= sec2 wcsc w 10. 2sin 2 y − 1 = 1 − 2cos2 y

11. sec y − tany sin y = cos y 12. 1 − cos2 θ( ) cot2 θ + 1( ) = 1

13.

1 − sin2 θ 1 + tan2θ

= cos4 θ 14.

sin t csc t

+ cos t sec t

= 1

15.

sin y + tan y 1 + sec y

= sin y 16.

1 − tan2 w 1 + tan2 w

= 2cos2 w − 1

Trig Identities worksheet 3.3

MCR 3U Worksheet – Transformations of Sinusoidal Functions Dec 3, 2019

Graph each function. The parent function, y=sin x or y=cos x , is shown as a dotted line.

(a) vertical stretch or compression sketch y= 2sin x

(b) horizontal stretch or compression sketch y=cos (3 x)

(c) vertical translation (or shift) sketch y=sin (x )+ 2

(d) horizontal translation (or phase shift) sketch one cycle of y=cos (x+ 90 ̊ )

(e) vertical reflection (about the x-axis) sketch y=−cos x

(f) horizontal reflection (about the y-axis) sketch one cycle of y=sin (−x )

Page 1 of 2.

(g) combination of transformations sketch y=2sin (12 x)−1

(h) combination of transformations sketch y= 1

2 cos (2 x )−1.5

Blank graphs for student practice y=sin x y=cos x

Unit 6: Periodic Functions Page 2 of 2.

MCR3U Determining Trigonometric Equations from Graphs May 27, 2019

A)

B)

C) D)

E) F)

rev. 18. May. 2011