BackIntroduction to Trigonometric Identities quiz
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1/15BackSkip to main contentBackWhich trigonometric functions are even and which are odd?
Cosine and secant are even functions; sine, tangent, cosecant, and cotangent are odd functions. What does it mean for a function to be even?
An even function satisfies f(-x) = f(x) and is symmetric about the y-axis. What does it mean for a function to be odd?
An odd function satisfies f(-x) = -f(x) and is symmetric about the origin. What is the even-odd identity for cosine?
cos(-θ) = cos(θ) What is the even-odd identity for sine?
sin(-θ) = -sin(θ) What is the even-odd identity for tangent?
tan(-θ) = -tan(θ) State the basic Pythagorean identity involving sine and cosine.
sin²θ + cos²θ = 1 How do you derive the identity tan²θ + 1 = sec²θ?
Divide the basic Pythagorean identity by cos²θ. How do you derive the identity 1 + cot²θ = csc²θ?
Divide the basic Pythagorean identity by sin²θ. When should you use even-odd identities in simplifying trigonometric expressions?
Use even-odd identities whenever the argument of a trig function is negative. What are the three criteria for a trigonometric expression to be fully simplified?
All arguments are positive, there are no fractions, and there are as few trig functions as possible. What strategy can you use if your expression contains 1 plus or minus a trig function in the denominator?
Multiply the numerator and denominator by the conjugate (1 minus or plus the trig function) to simplify. How do you simplify tan(-θ)·csc(θ)?
Rewrite tan(-θ) as -tan(θ), express in terms of sine and cosine, and simplify to -sec(θ). How do you verify a trigonometric identity?
Simplify one or both sides of the equation using identities and algebraic manipulation until both sides are equal. What is the result of sec²θ - tan²θ?
sec²θ - tan²θ = 1, by rearranging the Pythagorean identity tan²θ + 1 = sec²θ.
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