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Chapter 4: Problem 22

Find a cofunction with the same value as the given expression. $$\sin 19^{\circ}$$

Short Answer

Expert verified
The cofunction with the same value as \( \sin 19^{\circ} \) is \( \cos 71^{\circ} \).

Step by step solution

01

Identify the Complement of the Given Angle

To find the cofunction of \( \sin 19^{\circ} \), you first need to identify the complement of the given angle. This can be done by subtracting the given angle from 90 degrees, as complementary angles add up to 90 degrees: \( 90^{\circ} - 19^{\circ} = 71^{\circ} \)
02

Identify the Cofunction of the Given Expression

Next, identify the cofunction that corresponds to the sine function. In trigonometry, the cofunction of the sine function is the cosine function. Therefore, you need to find the value of cosine at the complementary angle which is \( \cos 71^{\circ} \).
03

Identify the Cofunction With the Same Value

Finally, you determine that \( \cos 71^{\circ} \) is the cofunction that generates the same value as \( \sin 19^{\circ} \).

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Most popular questions from this chapter

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

Use a vertical shift to graph one period of the function. $$y=\sin x+2$$

Without drawing a graph, describe the behavior of the basic cosine curve.

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 a graphing utility to graph $$ y=\sin x-\frac{\sin 3 x}{9}+\frac{\sin 5 x}{25} $$ in a \(\left[-2 \pi, 2 \pi, \frac{\pi}{2}\right]\) by [-2,2,1] viewing rectangle. How do these waves compare to the smooth rolling waves of the basic sine curve?
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