Answers TN-Algebra II B SC 26-27 For CreditEvaluating the Six Trigonometric Functions

Evaluating the Six Trigonometric Functions — Unit test Answers

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How long is the arc intersected by a central angle of radians in a circle with a radius of 6 ft? Round your answer to the nearest tenth. Use 3.14 for .

1.0 ft

5.7 ft

6.3 ft

7.0 ft

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What is the approximate length of arc s on the circle below? Use 3.14 for . Round your answer to the nearest tenth.

5.8 ft

6.3 ft

27.5 ft

69.1 ft

What are the exact values of the six trigonometric functions for radians?

sine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction; cosine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative one-half; tangent (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartRoot 3 EndRoot. Cosecant (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction; secant (Negative StartFraction 7 pi Over 6 EndFraction) = 2; Cotangent (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 3 EndFraction

sine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative one-half; cosine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction; tangent (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 3 EndFraction. Cosecant (Negative StartFraction 7 pi Over 6 EndFraction) = Negative 2; secant (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction; Cotangent (Negative StartFraction 7 pi Over 6 EndFraction) = StartRoot 3 EndRoot

sine (Negative StartFraction 7 pi Over 6 EndFraction) = one-half; cosine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction; tangent (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 3 EndFraction. Cosecant (Negative StartFraction 7 pi Over 6 EndFraction) = 2; secant (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction; Cotangent (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartRoot 3 EndRoot

sine (Negative StartFraction 7 pi Over 6 EndFraction) = StartFraction StartRoot 3 EndRoot Over 3 EndFraction; cosine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction; tangent (Negative StartFraction 7 pi Over 6 EndFraction) = StartRoot 3 EndRoot. Cosecant (Negative StartFraction 7 pi Over 6 EndFraction) = StartRoot 3 EndRoot; secant (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction; Cotangent (Negative StartFraction 7 pi Over 6 EndFraction) = StartFraction StartRoot 3 EndRoot Over 3 EndFraction

Melanie simplified the expression as shown below.Step 1:Step 2:Step 3:Step 4:In which step did Melanie make the first error, and which expression should she have written in that step?

step 1;

step 4; cos(x)

step 4; csc(x)

An angle in standard position measures radians, and P(0, 1) is on the terminal side of the angle. What is the value of the cosine of this angle?

–1

undefined

What is the value of x in the diagram below?

StartFraction 18 Over StartRoot 3 EndRoot EndFraction

StartFraction 18 StartRoot 2 EndRoot Over StartRoot 3 EndRoot EndFraction

StartFraction 18 StartRoot 3 EndRoot Over StartRoot 2 EndRoot EndFraction

18 StartRoot 2 EndRoot

In a right triangle, and . What is the approximate value of ?

0.329

0.376

1.288

2.659

For which value of is cot () undefined?

90º

180º

270º

450º

Which values for have the same reference angles?

, ,

A circle has a central angle measuring radians that intersects an arc of length 18 cm. What is the length of the radius of the circle? Round your answer to the nearest tenth. Use 3.14 for .

3.7 cm

4.9 cm

14.3 cm

15.4 cm

A student uses the equation to represent the speed, s, in feet per second, of a toy car driving around a circular track having an angle of incline , where . To solve the problem, the student used the given value of to find the value of and then substituted the value of in the equation above to solve for s. What is the approximate value of s, the speed of the car in feet per second?

5.3

7.5

9.2

28.3

A student is given that point P(a, b) lies on the terminal ray of angle , which is between radians and 2 radians. The student uses the steps below to find cos . Step 1Find the quadrant in which P(a, b) lies:P(a, b) is in Quadrant IV.Step 2Use the point and the Pythagorean theorem to determine the value of r:, but since r must be positive, .Step 3Determine cos ., where a and b are positive.Which of the following explains whether the student is correct?

The student made an error in step 3 because a is positive in Quadrant IV; therefore, .

The student made an error in step 3 because .

The student made an error in step 2 because r is negative in Quadrant IV; therefore, .

The student made an error in step 2 because using the Pythagorean theorem gives .

Henry is asked to find the exact value of . His steps are shown below.1. Subtract from as many times as possible: – = 2. Find the reference angle for : – = .3. The cosine value for is .4. The cosine value is positive because is in the first quadrant.Which of the following describes Henry’s errors?