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Chapter 4: Problem 92

Use words (not an equation) to describe one of the quotient identities.

Short Answer

Expert verified
In words, the quotient identity for tangent can be described as: The tangent of an angle equals the ratio of the sine of the angle to the cosine of the same angle. This remains true for any angle, provided the cosine of that angle is not zero.

Step by step solution

01

Identifying Quotient Identities

There are two fundamental quotient identities that directly relate to the tangent and cotangent trigonometric functions. They are: \( \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} \) and \( \cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)} \). Choose one of these to describe.
02

Describing the Chosen Identity in Words

Choosing the quotient identity for tangent, it can be described as follows: The tangent of an angle is the ratio of the sine of the angle to the cosine of the same angle. In other words, for any given angle, the tangent function output (the tangent of the angle) can be obtained by dividing the output of the sine function (the sine of the angle) by the output of the cosine function (the cosine of the angle). Note that cosine should never be zero, to avoid division by zero.

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When graphing one complete cycle of \(y=A \cos (B x-C)\) I find it easiest to begin my graph on the \(x\) -axis.

Determine the amplitude, period, and phase shift of each function. Then graph one period of the function. $$y=-4 \cos \left(2 x-\frac{\pi}{2}\right)$$

Use a graphing utility to graph each function. Use a viewing rectangle that shows the graph for at least two periods. $$y=\cot 2 x$$

Use a graphing utility to graph each pair of functions in the same viewing rectangle. Use a viewing rectangle that shows the graphs for at least two periods. $$y=-2.5 \sin \frac{\pi}{3} x \text { and } y=-2.5 \csc \frac{\pi}{3} x$$

Use the keys on your calculator or graphing utility for converting an angle in degrees, minutes, and seconds \(\left(D^{\circ} M^{\prime} S^{\prime \prime}\right)\) into decimal form, and vice versa. Convert each angle to a decimal in degrees. Round your answer to two decimal places. $$30^{\circ} 15^{\prime} 10^{\prime \prime}$$
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