Answers PrecalculusSolving Trigonometric Equations

Solving Trigonometric Equations — Unit test Answers

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

and

and

, , , and

, , , and

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Sameena measures the angle from the ground to the top of a building from two locations. The angle of elevation from the first point is 45°, and the angle of elevation from the second point is 60°. The distance from the second point to the top of the building is 150 ft. [Not drawn to scale]What is the distance from the first observation point to the top of the tower (x)? Round the answer to the nearest tenth.

122.5 ft

183.7 ft

244.9 ft

501.9 ft

Which equation represents a true sine ratio in ?

sine A = StartFraction b over c EndFraction

sine A = StartFraction h over c EndFraction

sine C = StartFraction b over a EndFraction

sine C = StartFraction a over h 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

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

sin(x)

1 – cos(x)

1 – cos2(x)

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

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

Review the proof.

step 2

step 4

step 6

step 8

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

sin(49°)

cos(49°)

sin(157°)

cos(157°)

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

–1

Negative one-half

What is the range of ?

and

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

Let where 0° ≤ x ≤ 180°. What are the possible values for x?

45° only

135° only

45° or 225°

135° or 315°

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°}

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

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)

Which is equivalent to ? Give your answer in radians.

mc026-2.jpg

mc026-3.jpg

mc026-4.jpg

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 equation below is equivalent to ?

h = StartFraction sine C over a EndFraction

a = h sine C

a = StartFraction sine C over h EndFraction

h = a sine C

Two trains leave a station on different tracks. The tracks make an angle of 130°, with the station as a vertex. The first train travels 100 km and makes its first stop at point A, while the second train travels 200 km and makes it first stop at point B. How far apart are the trains when both are at their first stop? Round the answer to the nearest integer. [Not drawn to scale]