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	College Algebra with Trigonometry 6/e Barnett/Ziegler/Byleen
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Chapter 6: Trigonometric Functions

Worked Exercises

Chapter 6: Trigonometric Functions

Exercise Set 6-1

In all problems, if angle measure is expressed by a number that is not in degrees, it is assumed to be in radians.

Find the degree measure of the angle, keeping in mind that an angle of one complete rotation corresponds to 360°.

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Find the radian measure of a central angle opposite an arc s in a circle of radius r, where r and s are as given.

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Find the radian measure of the angle, keeping in mind that an angle of one complete rotation corresponds to 2 radians.

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Find the exact radian measure of the angle, in terms of .

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Find the exact degree measure of the angle.

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Convert the angle to decimal degrees to three decimal places.

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Convert the angle to degree-minute-second form.

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Indicate whether the angle is a I, II, III or IV quadrant angle or a quadrantal angle. The angle is in standard position in a rectangular coordinate system. (A sketch may be of help).

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Determine if the angle is coterminal with 30° if it is placed in standard position in a rectangular coordinate system.

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Determine if the angle is coterminal with 3/4 if it is placed in standard position in a rectangular coordinate system.

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Exercise Set 6-2

Solve the triangle using the information given.

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Exercise Set 6-3

Find the value of the trigonometric function for an angle that has a terminal side containing the given point.

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Find the value of the trigonometric function for an angle (without finding ). Sketching a reference triangle should be helpful.

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Find the exact value of the trigonometric function for an angle that has a terminal side containing the given point.

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Find the exact value of the trigonometric function for an angle (without finding ). Sketching a reference triangle should be helpful.

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Figure for 65.
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Exercise Set 6-4

Evaluate axactly without using a calculator or table. If the answer involves a radical, leave it in exact radical form.

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Find the smallest positive in degree measure for which:

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Find the smallest positive real number for which:

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Find exact values of x and y.

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Exercise Set 6-5

The figure below may be useful in a number of problems in this exercise:

Find the coordinates of the circular point P for the indicated values of x by referring to the given figure. Do not use a calculator.

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Find the exact values of x from the indicated interval that satisfy the equation or condition. Refer to the figure.

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Evaluate exactly without a calculator or table.

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Simplify the expression using appropriate basic idgraphics/entities.

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Indicate whether the function is symmetric with respect to the x axis, y axis, or origin.

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Exercise Set 6-6

The figure below will be useful in many of the problems in this exercise

Answer the problem without looking back in the text or using a graphing utility. You can refer to the given figure.

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Exercise Set 6-7

State the amplitude A and period P of the function, and graph the function over the indicated interval.

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Find the equation of the form y = A sin Bx that produces the graph shown.

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Find the equation of the form y = cos Bx that produces the graph shown.

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State the amplitude A, period P, and phase shift of the function, and graph the function over the indicated interval.

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Exercise Set 6-8

Find the period of the function, and graph the function for the indicated interval.

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Find the period and phase shift, then graph the function.

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Exercise Set 6-9

Find exact values without using a calculator.

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Write the expression as an algebraic expression in x free of trigonometric or inverse trigonometric functions.

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Find f^-1(x). How must x be restricted in f^-1(x)?

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