Patrick Jones - Calculus - 1001 Practice Problems For Dummies (+ Free Online Practice)

96.

97.

98–102Use polynomial long division to divide.

98.

99.

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101.

102.

Chapter 2

In addition to having a strong algebra background, you need a strong trigonometry skill set for calculus. You want to know the graphs of the trigonometric functions and to be able to evaluate trigonometric functions quickly. Many calculus problems require one or more trigonometric identities, so make sure you have more than a few of them memorized or at least can derive them quickly.

In this chapter, you solve a variety of fundamental trigonometric problems that cover topics such as the following:

Understanding the trigonometric functions in relation to right triangles

Finding degree and radian measure

Finding angles on the unit circle

Proving identities

Finding the amplitude, period, and phase shift of a periodic function

Working with inverse trigonometric functions

Solving trigonometric equations with and without using inverses

Remember the following when working on the trigonometry review questions:

Being able to evaluate the trigonometric functions at common angles is very important since they appear often in problems. Having them memorized will be extremely useful!

Watch out when solving equations using inverse trigonometric functions. Calculators give only a single solution to the equation, but the equation may have many more (sometimes infinitely many solutions), depending on the given interval. Thinking about solutions on the unit circle is often a good way to visualize the other solutions.

Although you may be most familiar with using degrees to measure angles, radians are used almost exclusively in calculus, so learn to love radian measure.

Memorizing many trigonometric identities is a good idea because they appear often in calculus problems.

103–104Evaluate , , and for the given right triangle. Remember to rationalize denominators that contain radicals.

103.

104.

105–108Evaluate the trig function. Remember to rationalize denominators that contain radicals.

105. Given , where , find .

106. Given , where , find .

107. Given , where and , find .

108. Given , where , find .

109–112Convert the given degree measure to radian measure.

109. 135°

110.

111. 36°

112.

113–116Convert the given radian measure to degree measure.

113. rad

114. rad

115. rad