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
MCR3U Trig 08 WS Solving Trig Equations & CAST Rule
WS – Trig Identities
MCR3U – Periodic 03 – WS – Graphing Transformations
MCR3U – Periodic 05 – WS – Equations from Graphs
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