Practice Pythagorean Identities (3.1) - Trigonometric Identities and Graphs

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6 sample questions

Question 1.
Prove that sin²(θ) + cos²(θ) = 1.
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Recall the definitions of sine and cosine.
Question 2.
If cos²(θ) = 0.36, what is sin²(θ)?
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Use the Pythagorean identity.
3Question 3.
What is the first Pythagorean identity?
- sin²θ + cos²θ = 1
- 1 + tan²θ = sec²θ
- 1 + cot²θ = cosec²θ
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Think about sine and cosine.
4Question 4.
True or False: 1 + tan²θ = sec²θ relates tangent to sine.
- True
- False
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Consider what each term represents.
Question 5.
If sin(θ) = 0.6, derive cos(θ) and verify using the Pythagorean identity.
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Remember sine and cosine can have positive and negative values, depending on the quadrant.
Question 6.
Prove that 1 + tan²(θ) = sec²(θ) by using the first Pythagorean identity.
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Think about the definitions of tangent and secant.

6 more questions in this section. Enroll free to practise them all.