Practice Example 1: Prove The Identity (9.1) - Trigonometric Identities and Graphs

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6 sample questions

Question 1.
Verify that sin²θ + cos²θ = 1 when θ = 60°.
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Square each exact value before adding.
Question 2.
If cos²θ = 0.36, find sin²θ.
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Rearrange the identity.
3Question 3.
What does sin²θ mean?
- (sin θ)²
- sin(θ²)
- 2 sin θ
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Which part is being squared?
4Question 4.
Why does checking sin²θ + cos²θ = 1 at θ = 30° not prove the identity?
- An identity must hold for every angle and one example cannot show that
- 30° is not a special angle
- The calculation at 30° gives the wrong answer
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How many angles does an identity talk about?
Question 5.
Prove that sin⁴θ − cos⁴θ = sin²θ − cos²θ.
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sin⁴θ is (sin²θ)².
Question 6.
Prove that 1 + tan²θ = 1/cos²θ (for cos θ ≠ 0), and check it at θ = 45°.
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Divide the Pythagorean identity by cos²θ.

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