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Chapter 6 – Previous Provincial Exam Questions 1. State the exact value of cos

2. Prove the identity =

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3. Given sin 𝛼 = , where 𝛼 is in quadrant I, and sec 𝛽 = , where 𝛽 is in quadrant IV,

find the exact value of sin(𝛼 +𝛽) 4.Evaluate the expression sin 45° cos 15° − cos 45° sin 15° 5. Determine all the non-permissible values of 𝜃 over the interval [0, 2𝜋]. 𝑠𝑖𝑛𝜃

1 + cos 𝜃+ csc 𝜃 + cot 𝜃

Explain your reasoning.

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6. Given sin 𝛼 =√ , where 𝛼 is in quadrant II, and cos 𝛽 = − , where 𝛽 is in quadrant

III, a) find the exact value of tan(𝛼 − 𝛽) b) find the exact value of cot(𝛼 − 𝛽)

7. Determine the exact value of 4 cos

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8. Prove the identity for all permissible values of x = cot 𝑥

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9. Solve the following equation over the interval [0, 2𝜋] 2 cos 2𝜃 − 1 = 0 10. Solve the following equation algebraically for x, where 0 ≤ 𝑥 ≤ 2𝜋 2 cos 𝑥 = −3 sin 𝑥

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11. a) Prove the identity for all permissible values of 𝜃

= tan 𝜃 + 3

b) Determine all the non permissible values for 𝜃

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12. Prove the identity for all permissible values of 𝜃

= csc 𝜃 −

13. Explain the error that was made when solving the following equation sin 2𝜃 = cos 𝜃, where 𝜃 ∈ ℝ

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14. Prove the identity is true for all permissible values of x sec 𝑥 + tan 𝑥 =

15. Given the equation 2 sin 𝜃 − 3 sin 𝜃 + 1 = 0, verify that 𝜃 = is a solution.

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16. Solve the following equation algebraically where 180° ≤ 𝜃 ≤ 360° 2 sin 𝜃 + 5 cos 𝜃 + 1 = 0 17. Evaluate 2 sin cos [1 Mark]

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18. a) Verify that the equation = is true for 𝑥 =

b) Explain why verifying the equation for 𝑥 = is insufficient the conclude that the

equation is an identity. 19. Determine the exact value of tan 75° [2 Marks]

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20. a) Express in terms of csc 𝜃 only. You must completely simplify your answer.

b) Determine the exact value of the expression above when 𝜃 =

21. A non-permissible value of x for the function 𝑓(𝑥) = is [1 Mark]

a) −1 b) 0 c) 𝜋 d)

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22. Prove the following identity = sin 2𝑥

23. Given that cos 𝛼 = and sin 𝛼 < 0, find the exact value of tan(2𝛼)

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24. Prove the following identity

=

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25. Prove the identity for all permissible values of x

= cos 𝑥 − cos 𝑥

26. Given an example using values for A and B, in degrees or radians, to verify that cos(𝐴 + 𝐵) = cos 𝐴 + cos 𝐵 is NOT and identity.

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27. Prove the identity for all permissible values of 𝜃

= cos 2𝜃

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28. Prove the identity below for all permissible values of 𝜃 [3 Marks]

sin 𝜃 + =

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29. Given that cos 𝛼 = where 𝛼 is in quadrant IV, and sin 𝛽 = where 𝛽 is in quadrant

I, determine the exact value of [4 Marks] a) sin(𝛼 − 𝛽) b) csc(𝛼 − 𝛽) 30. Solve the following equation algebraically for 𝜃, where 0 ≤ 𝜃 ≤ 2𝜋 [4 Marks] 2 cos 2𝜃 = 1

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31. Prove he identity for all permissible values of 𝜃 [3 Marks]

cos 𝜃 + tan𝜃 sin 𝜃 =