6. Trigonometric Identities and More Equations

Use identities to correctly complete each sentence.

If cos θ = 0.8 and sin θ = 0.6, then tan(-θ) = ________________.

Find sin θ.

cos θ = 5/6, θ in quadrant I

Find sinθ.

cot θ = -1/3, θ in quadrant IV

Find sinθ.

cos (-θ) = (√3)/6, cot θ < 0

Find sinθ.

tan θ = -(√7)/2, sec θ > 0

Find sinθ.

sec θ = 7/2, tan θ < 0

Find sinθ.

csc θ = -8/5

Identify the basic trigonometric function graphed, and determine whether it is even or odd.

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Identify the basic trigonometric function graphed, and determine whether it is even or odd.

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Find the remaining five trigonometric functions of θ.

cos θ = 1/5, θ in quadrant I

Find the remaining five trigonometric functions of θ.

csc θ = -5/2, θ in quadrant III

Find the remaining five trigonometric functions of θ.

sin θ = -4/5, cos θ < 0

Find the remaining five trigonometric functions of θ.

cos θ = -1/4, sin θ > 0

Concept Check Does there exist an angle θ with the function values cos θ = ⅔ and sin θ = ¾?

In Exercises 63–68, find the exact value of each expression. Do not use a calculator. csc 37° sec 53° - tan 53° cot 37°