Pre-Calc/Trig Unit 3: Analytic Trig and Applications/5.1 Fundamental Identities Use the fundamental identities to find the value of the trigonometric ... Use the fundamental identities to find the value of the trigonometric function.

Find csc θ if sin θ = -

and θ is in quadrant IV.

]]> -

]]>

]]> Use the fundamental identities to find the value of the trigonometric ... Use the fundamental identities to find the value of the trigonometric function.

Find cos θ if sin θ = -

and θ is in quadrant III.

]]> -

]]>

]]> Write the expression in terms of sine and cosine, and simplify so that no ... Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.

]]> Correct

]]> csc x

]]> Incorrect. Think "Pythagorean Identity".

]]> 1

]]> Incorrect. Think "Pythagorean Identity".

]]> -sec x

]]> Incorrect. Think "Pythagorean Identity".

]]> Incorrect. Re-write in terms of sin and cos, then simplify.

]]> cot²x

]]> Correct

]]> csc²x

]]> Incorrect. Re-write in terms of sin and cos, then simplify.

]]> 1

]]> Incorrect. Re-write in terms of sin and cos, then simplify.

]]> Pre-Calc/Trig Unit 3: Analytic Trig and Applications/5.2 Verifying Trig Identities Perform the indicated operations and simplify the result.tan θ(cot θ - cos θ) Perform the indicated operations and simplify the result.

tan θ(cot θ - cos θ)

]]> 1.0000000 0.3333333 0 true true abc 1

]]> Incorrect. Distribute, then change to "sin" and "cos" before simplifying.

]]> - sec²θ

]]> Incorrect. Distribute, then change to "sin" and "cos" before simplifying.

]]> 0

]]> Incorrect. Distribute, then change to "sin" and "cos" before simplifying.

]]> 1 - sin θ

]]> Correct.

]]> Simplify the expression.sin θ cos θ sec θ csc θ Simplify the expression.

sin θ cos θ sec θ csc θ

]]> 1.0000000 0.3333333 0 true true abc sec²θ

]]> Incorrect. Change to "sin" and "cos"

]]> csc²θ

]]> Incorrect. Change to "sin" and "cos"

]]> 1

]]> Correct

]]> tan²θ

]]> Incorrect. Change to "sin" and "cos"

]]> Simplify the expression.sin2 x(cot2 x + 1) Simplify the expression.

sin² x(cot² x + 1)

]]> 1.0000000 0.3333333 0 true true abc cos² x + 1

]]> Incorrect. Substitute something in for (cot² x + 1)

]]> tan² x

]]> Incorrect. Substitute something in for (cot² x + 1)

]]> 1

]]> Correct

]]> -1

]]> Incorrect. Substitute something in for (cot² x + 1)

]]> Solve the problem.A wooden block sitting at rest on a flat, level board will ... Solve the problem.

A wooden block sitting at rest on a flat, level board will just begin to slide when the board is tilted up to a critical angle of inclination, θ_s . An experiment that determines this critical angle can be used to find the coefficient of static friction, μ_s , for the block on the board by using the relation

Rewrite this relation using a quotient identity.]]> 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 1.0000000 0.3333333 0 true true abc s = tan θ_s]]> Correct s = tan² θ_s]]> Incorrect s = cot θ_s]]> Incorrect s = sec θ_s]]> Incorrect Use the fundamental identities to simplify the expression. Use the fundamental identities to simplify the expression.