U7 ASSIGNMENT_TRIG_IDENTITIES_AND_EQUATIONS
S1-MHF4U1-11
Name:______________________________
U7A-(Lesson 1-5) Due date: January 17, 2023 @ 6:30 pm
Ultimate Due Date: January 18, 2023 @ 6:30 pm
UNIT 7 – ASSIGNMENT
Trigonometric Identities and Equations
TOTAL MARK: / 33
Instructions: Show all work for full marks. Add space if you need to.
Submit ONE FILE (PDF) under Unit 7 Assignment Folder in BrightSpace.
A. Knowledge/Understanding
1. a) Find the exact value of . You must have exact values, no decimals. [3]
csc 3Ï€4 tan
5Ï€
4
sec π6 cos
2Ï€
3
) Use a compound angle formula to determine an exact value of . [3]sin
11Ï€
12
2. Simplify: [2]
cos(π + ?) cos( ?2 − ?) − sin(π + ?) sin(? +
3?
2 )
S1-MHF4U1-11
Name:______________________________
U7A-(Lesson 1-5) Due date: January 17, 2023 @ 6:30 pm
Ultimate Due Date: January 18, 2023 @ 6:30 pm
3. Given that and , such that both x and y are in the same quadrant.sin ? = 35 cos ? =−
14
17
Without finding x and y, determine the exact values of the following trigonometric expression. [3]
Show all necessary diagrams on the right. [2]
csc (x + y)
B) Application
4. Consider and?(?) =
tan( ?+1)
csc ? ?(?) = sin ?
a) Identify any non-permissible values of x for each function. [2]
S1-MHF4U1-11
Name:______________________________
U7A-(Lesson 1-5) Due date: January 17, 2023 @ 6:30 pm
Ultimate Due Date: January 18, 2023 @ 6:30 pm
) Show the equation is true for x = . Is this sufficient evidence to conclude that
tan (?+1)
csc ? = sin ? π
the equation is identity? Why or why not? [2]
c) Use graphing technology to graph both . Can we conclude that:?(?) & ?(?)
is an identity? Explain? Attach the graph. [3]
tan (?+1)
csc ? = sin ?
d) Alge
aically prove is an identity for all permissible values. [3]
tan (?+1)
csc ? = sin ?
S1-MHF4U1-11
Name:______________________________
U7A-(Lesson 1-5) Due date: January 17, 2023 @ 6:30 pm
Ultimate Due Date: January 18, 2023 @ 6:30 pm
5. A fe
is wheel completes 2 revolutions in 90 seconds. Determine how far it has travelled in 30
seconds. The radius of the fe
is wheel is 8 m. [2]
C) Thinking/Inquiry
6. Prove the following identity: [4]
1−cos ?
sin ? =
sin ?
1+cos ?
7. Solve the following equation on the interval [4]2 sin 4? + sin 2? + 1 = 0 0 ≤ ? ≤ 2π.