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Chapter 4: Problem 91

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

Short Answer

Expert verified
One of the reciprocal identities is between sine and cosecant. For any angle, the reciprocal of the sine of the angle gives the cosecant of that angle.

Step by step solution

01

Understanding reciprocal identities

Reciprocal identities in trigonometry are mathematical consistencies where the reciprocal of a primary trigonometric ratio yields a different trigonometric ratio. The three primary trigonometric ratios are sine (sin), cosine (cos), and tangent (tan), and their reciprocals are cosecant (csc), secant (sec), and cotangent (cot), respectively.
02

Choose one and explain

Let's choose the reciprocal identity of sine. The reciprocal of sine is cosecant. This means that for any angle in a right triangle, the ratio of the hypotenuse to the side opposite that angle (which is the definition of sine) is the reciprocal of the ratio of the side opposite to the hypotenuse (which is the definition of cosecant). This can be condensed into a simple rule: \( csc(\Theta) = \frac{1}{sin(\Theta)} \).

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Most popular questions from this chapter

Explain how to find the length of a circular arc.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I made an error because the angle I drew in standard position exceeded a straight angle.

What does a phase shift indicate about the graph of a sine function? How do you determine the phase shift from the function's equation?

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. $$y=0.8 \sin \frac{x}{2} \text { and } y=0.8 \csc \frac{x}{2}$$

Use a graphing utility to graph each function. Use a viewing rectangle that shows the graph for at least two periods. $$y=\frac{1}{2} \tan \pi x$$
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