Answers 191 FT B 2742Unit Test

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Which expression is equivalent to cos(103°)cos(54°) – sin(103°)sin(54°)?

sin(49°)

cos(49°)

sin(157°)

cos(157°)

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Which shows all the exact solutions of ? Give your answer in radians.

and

and

, , , and

, , , and

What is the exact value of

StartFraction 1 Over 2 + StartRoot 3 EndRoot EndFraction

StartFraction 1 Over StartRoot 3 EndRoot EndFraction

StartFraction 3 Over StartRoot 3 EndRoot EndFraction

StartFraction 1 Over 2 minus StartRoot 3 EndRoot EndFraction

For 0° ≤ x < 360°, what are the solutions to cos – sin(x) = 0?

{0°, 60°, 300°}

{0°,120°, 240°}

{60°, 180°, 300°}

{120°,180°, 240°}

Which values represent solutions to the equation? where x [0, ]

{0,}

Left-brace 0, StartFraction pi Over 2 EndFraction, pi Right-brace

Left-brace, 0, pi, 2 pi Right-brace

Left-brace 0, StartFraction pi Over 2 EndFraction, pi StartFraction 3 pi Over 2 EndFraction Right-brace

Solve: over the interval .

StartFraction pi Over 2 EndFraction

StartFraction 2 pi Over 3 EndFraction

StartFraction 3 pi Over 4 EndFraction

StartFraction 5 pi Over 6 EndFraction

Which is equivalent to ? Give your answer in radians.

mc026-2.jpg

mc026-3.jpg

mc026-4.jpg

Review the proof of .tan(A – B) =Step 1: Step 2: Step 3: Step 4:

cos(A)cos(B)

cos(A)sin(B)

sin(A)cos(B)

sin(A)sin(B)

What is expressed as a single trigonometric ratio?

–tan(20°)

–tan(5°)

tan(5°)

tan(20°)

Review the following derivation of the tangent double angle identity. The steps are not listed in the correct order.

4, 3, 5, 1, 2

4, 5, 3, 1, 2

3, 4, 5, 1, 2

3, 4, 1, 5, 2

Which expression is equivalent to (1 + cos(x))2?

sin(x)

1 – cos(x)

1 – cos2(x)

(1 + cos(x))(sin(x))

What is the exact value of sin(264°)cos(6°) + cos(264°)sin(6°)?

–1

Negative one-half

Review the proof.

step 2

step 4

step 6

step 8

What is the range of ?

and

Review the incomplete steps in the derivation of the tangent sum identity.Which action can be taken to the expression in Step 3 to give an expression for Step 4?

divide both the numerator and denominator by sin(x)sin(y)

divide both the numerator and denominator by sin(x)cos(y)

divide both the numerator and denominator by cos(x)sin(y)

divide both the numerator and denominator by cos(x)cos(y)

Suppose and cos(x) < 0. What the value of cos(2x)?

Negative StartFraction 16 Over 25 EndFraction

Negative StartFraction 7 Over 25 EndFraction

StartFraction 7 Over 25 EndFraction

StartFraction 16 Over 25 EndFraction

Given: What is the value of ?

StartFraction StartRoot 15 EndRoot + 1 Over 1 minus StartRoot 15 EndRoot EndFraction

StartFraction negative StartRoot 15 EndRoot + 1 Over 1 + StartRoot 15 EndRoot EndFraction

StartFraction StartRoot 15 EndRoot + 1 Over 1 + StartRoot 15 EndRoot EndFraction

StartFraction negative StartRoot 15 EndRoot minus 1 Over 1 minus StartRoot 15 EndRoot EndFraction

Which expression is equivalent to tan(x – )?

StartFraction tangent (x) minus tangent (pi) Over 1 minus (tangent (x) ) (tangent (pi) ) EndFraction

StartFraction tangent (x) minus tangent (pi) Over 1 + (tangent (x) ) (tangent (pi) ) EndFraction

StartFraction tangent (x) + tangent (pi) Over 1 minus (tangent (x) ) (tangent (pi) ) EndFraction

StartFraction tangent (x) + tangent (pi) Over 1 + (tangent (x) ) (tangent (pi) ) EndFraction

An object is attached to a spring that is stretched and released. The equation models the distance, d, of the object in inches above or below the rest position as a function of time, t, in seconds. Approximately when will the object be 6 inches above the rest position? Round to the nearest hundredth, if necessary.