U7 ASSIGNMENT_TRIG_IDENTITIES_AND_EQUATIONSS1-MHF4U1-11Name:______________________________U7A-(Lesson 1-5) Due date: January 17, 2023 @ 6:30 pmUltimate Due Date: January 18, 2023 @ 6:30...

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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 3π4 tan 5π 4 sec π6 cos 2π 3 b) Use a compound angle formula to determine an exact value of . [3]sin 11π 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 b) 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) Algebraically 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 ferris wheel completes 2 revolutions in 90 seconds. Determine how far it has travelled in 30 seconds. The radius of the ferris 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.