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Chapter 4: Problem 72

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The sine and cosine are cofunctions and reciprocals of each other.

Short Answer

Expert verified
The statement 'The sine and cosine are cofunctions and reciprocals of each other.' only makes partial sense. They are cofunctions of each other, but they are not reciprocals of each other.

Step by step solution

01

Understand trigonometric functions

In trigonometry, sine and cosine are fundamental functions. They are not reciprocals of each other. Reciprocal of sine is cosecant, and reciprocal of cosine is secant. Therefore, the part of the statement saying they are reciprocals is incorrect.
02

Analyze cofunctions

The term 'cofunction' in trigonometry refers to functions where for all acute angles, their function values add up to 90 degrees. Sine and Cosine are indeed cofunctions because sin(x) = cos(90掳 - x), they satisfy the cofunction identity. Therefore, the part of the statement saying they are cofunctions is correct.

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Most popular questions from this chapter

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. $$y=-3.5 \cos \left(\pi x-\frac{\pi}{6}\right) \text { and } y=-3.5 \sec \left(\pi x-\frac{\pi}{6}\right)$$

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 \(D^{\circ} M^{\prime} S^{\prime \prime}\) form. Round your answer to the nearest second. $$30.42^{\circ}$$

will help you prepare for the material covered in the next section. $$\text { Simplify: } \frac{-\frac{3 \pi}{4}+\frac{\pi}{4}}{2}$$

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

Graph \(y=\sin \frac{1}{x}\) in a [-0.2,0.2,0.01] by [-1.2,1.2,0.01] viewing rectangle. What is happening as \(x\) approaches 0 from the left or the right? Explain this behavior.
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