Answers PrecalculusSolving Trigonometric Equations

Solving Trigonometric Equations — Unit test Answers

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Which is the graph of ?

A smooth curve resembling an arctangent function. The x-axis ranges from -6 to 6, and the y-axis from -p to p. The curve approaches horizontal asymptotes at y = p/2 and y = -p/2, passing through the origin.

A graph of a function with asymptotic behavior. The x-axis ranges from -5 to 5, and the y-axis ranges from -p to p. The curve is located in the fourth quadrant, approaching the y-axis asymptotically as x approaches zero from both positive and negative directions. The curve also approaches zero asymptotically as x moves away from zero in both directions. The function does not intersect either axis.

A graph of a function with the x-axis ranging from -2.5 to 2.5 and the y-axis ranging from -p to p. The curve passes through the origin (0,0) and changes direction at y=0. It intersects the x-axis at two points, approximately at x=-1 and x=1. The curve is symmetric about the origin.

The image shows a mathematical graph plotted on a Cartesian coordinate system. The x-axis ranges from -2 to 2, and the y-axis ranges from -p to p. A smooth, continuous curve intersects the x-axis at approximately 1. The curve extends into both the positive and negative quadrants. The point p is labeled on the positive y-axis and -p on the negative y-axis.

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Review the diagram of the unit circle.

StartRoot (cosine (u + v) minus 1) squared + (sine (u + v) minus 0) squared EndRoot = StartRoot (cosine (u) minus 1) squared minus (sine (u) minus 0) squared EndRoot

StartRoot (cosine (u + v) minus 1) squared + (sine (u + v) minus 0) squared EndRoot = StartRoot (cosine (negative v) minus 1) squared + (sine (negative v) minus 0) squared EndRoot

StartRoot (cosine (u + v) minus 1) squared + (sine (u + v) minus 0) squared EndRoot = StartRoot (cosine (u) minus cosine (negative v) ) squared + (sine (u) minus sine (negative v)) squared

StartRoot (cosine (u + v) minus 1) squared + (sine (u + v) minus 0) squared EndRoot = StartRoot (cosine (u + v) minus cosine (u) ) squared + (sine (u + v) minus sine (u)) squared EndRoot

Which expression is equivalent to ?

Cosine (negative StartFraction pi Over 3 EndFraction)

Sine (negative StartFraction pi Over 3 EndFraction)

Cosine (StartFraction pi Over 2 EndFraction)

Sine (StartFraction pi Over 2 EndFraction)

Review the proof.

1 – cos(x)

1 + cos(x)

StartRoot 1 minus cosine (x) EndRoot

StartRoot 1 + cosine (x) EndRoot

The motion of a weight that hangs from a spring is represented by the equation . It models the weight’s height, h, in inches above or below the rest position as a function of time, t, in seconds. Approximately when will the object be 4 inches below the rest position? Round to the nearest hundredth, if necessary.

0 seconds

0.29 seconds

0.39 seconds

1.95 seconds

What is the exact value of sin(105°)?

Negative StartFraction StartStartRoot 2 minus StartRoot 3 EndRoot EndEndRoot Over 2 EndFraction

Negative StartFraction StartStartRoot 2 + StartRoot 3 EndRoot EndEndRoot Over 2 EndFraction

StartFraction StartStartRoot 2 minus StartRoot 3 EndRoot EndEndRoot Over 2 EndFraction

StartFraction StartStartRoot 2 + StartRoot 3 EndRoot EndEndRoot Over 2 EndFraction

What is the exact value of tan(195°)?

StartFraction StartRoot 3 EndRoot + 1 Over 1 minus StartRoot 3 EndRoot EndFraction

StartFraction StartRoot 3 EndRoot minus 3 Over 3 + StartRoot 3 EndRoot EndFraction

StartFraction StartRoot 3 EndRoot minus 1 Over 1 + StartRoot 3 EndRoot EndFraction

StartFraction StartRoot 3 EndRoot + 3 Over 3 minus StartRoot 3 EndRoot EndFraction

Which pair of equations below is a result of constructing the altitude, h, in ?

sine A = StartFraction h over c EndFraction sine C = StartFraction h over a EndFraction

sine A = StartFraction h over c EndFraction sine B = StartFraction b over c EndFraction

sine A = StartFraction b over c EndFraction sine C = StartFraction b over a EndFraction

sine C = StartFraction h over a EndFraction sine B = StartFraction b over a EndFraction

Which statement is true about the graph of the equation ?

There is a horizontal asymptote at .

There is a vertical asymptote at .

Which function is equivalent to the inverse of ?

mc020-2.jpg

mc020-3.jpg

mc020-4.jpg

mc020-5.jpg

For what values of x is the trigonometric equation tan(x − 180°) − sin(x − 180°) = 0, where 0 ≤ x < 360°, true?

{0°, 90°}

{0°, 180°}

{90°, 180°}

{90°, 270°}

Review the proof of cos(A - B) = cosAcosB + sinAsinB.Step 1: Step 2: Step 3: Step 4: Step 5:Step 6:Step 7:

1 and 1

2 and 1

(cosAcosB)2(sinAsinB)2 and (cos2(A – B))((sin2(A – B))

(cos2A + sin2A)(cos2B + sin2B) and (cos2(A – B))(sin2(A – B))

For , which expression is equivalent to ?

StartFraction 1 Over StartRoot 2 (1 + cosine x) EndRoot EndFraction

StartFraction 1 Over StartRoot 2 (1 minus cosine x) EndRoot EndFraction

(StartRoot StartFraction 1 + cosine (x) Over 2 EndFraction EndRoot) (StartFraction 1 Over 1 minus cosine (x) EndFraction)

(StartFraction 1 + cosine (x) Over StartRoot 2 (1 minus cosine x) EndRoot EndFraction) (StartFraction 1 Over 1 minus cosine (x) EndFraction)

Solve the Law of Cosine: for cos C.

cosine C = StartFraction square of a + square of b minus square of c over 2ab EndFraction

cosine C = StartFraction square of a + square of b + square of c over negative 2ab EndFraction

cosine C = StartFraction square of c minus square of a minus square of b over 2ab EndFraction

cosine C = StartFraction square of negative c + square of a + square of b over negative 2ab EndFraction

What are the solutions to the equation over the interval [0, 2]?

only

StartFraction pi Over 6 EndFraction, StartFraction 5 pi Over 6 EndFraction, StartFraction 7 pi Over 6 EndFraction and StartFraction 11 pi Over 6 EndFraction

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Solving Trigonometric Equations — Unit test Answers

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