Using identities to simplify expressions and prove results (HSC SSCE Mathematics Extension 1): Flashcards
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What is a trigonometric identity?
What is a trigonometric identity?
An equation with trig functions true for all values.
What is the Pythagorean identity?
What is the Pythagorean identity?
sin²θ + cos²θ = 1.
What does the reciprocal identity for sine state?
What does the reciprocal identity for sine state?
sinθ = 1/cscθ and cscθ = 1/sinθ.
What is the quotient identity for tangent?
What is the quotient identity for tangent?
tanθ = sinθ/cosθ.
How do you simplify 1 + tan²θ?
How do you simplify 1 + tan²θ?
Replace tan²θ with sec²θ - 1 to get sec²θ.
What is the fundamental identity in trigonometry?
What is the fundamental identity in trigonometry?
cos²θ + sin²θ = 1 is the fundamental identity.
What is a common mistake with sin(-θ)?
What is a common mistake with sin(-θ)?
Incorrectly stating sin(-θ) = sinθ.
What is the correct form of sin(-θ)?
What is the correct form of sin(-θ)?
sin(-θ) = -sinθ.
How do you solve 2sin²θ - 1 = 0?
How do you solve 2sin²θ - 1 = 0?
Find θ = π/4 + nπ or 3π/4 + nπ.
Why are trigonometric identities essential?
Why are trigonometric identities essential?
They simplify expressions and prove results.