Practice Practice Problems (10) - Trigonometric Identities and Graphs - IB 10 Mathematics

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6 sample questions

Question 1.
Prove the identity sin²θ + cos²θ = 1.
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Think about the definitions of sine and cosine on the unit circle.
Question 2.
Calculate sin(45°) and cos(45°).
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Use the angles of a 45-45-90 triangle.
3Question 3.
What is the identity for 1 + tan²θ?
- sin²θ
- sec²θ
- cos²θ
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Think about how tan relates to sin and cos.
4Question 4.
Is sin(x) a periodic function?
- True
- False
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Recall the periodic nature of sine functions.
Question 5.
Prove that 1 + cot²θ = csc²θ.
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Recall how cotangent and cosecant relate to sine and cosine.
Question 6.
Given the equation sin²x + cos²x = 1, derive the values for sin(x) if cos(x) = 1/2.
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Think about the definition of a triangle in relation to the unit circle.

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