Practice Fundamental Trigonometric Identities (3) - Trigonometric Identities and Graphs

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6 sample questions

Question 1.
What is sin²θ + cos²θ?
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This is derived from the Pythagorean identity.
Question 2.
If sec(θ) = 2, what is cos(θ)?
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Recall the reciprocal identity involving secant.
3Question 3.
What is the fundamental Pythagorean identity?
- sin²θ + cos²θ = 1
- tan²θ + cot²θ = 1
- sec²θ + cot²θ = csc²θ
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Remember it as the basis of all trigonometric identities.
4Question 4.
True or False: Reciprocal identities state that sin(θ) = cosec(θ).
- True
- False
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Define the relationship carefully to clarify.
Question 5.
Prove that tan²(θ) + 1 = sec²(θ) using the unit circle.
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Refer back to the definitions of sine and cosine in terms of the unit circle.
Question 6.
Using the identity sin²(θ) + cos²(θ) = 1, show that if sin(θ) = 4/5, then cos(θ) must equal 3/5.
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Make sure to square the sine term appropriately.

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