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Chapter 4: Problem 31

Use a calculator to evaluate each function. Round your answers to four decimal places. (Be sure the calculator is in the correct mode.) (a) \(\sin 10^{\circ}\) (b) \(\cos 80^{\circ}\)

Short Answer

Expert verified
The solution for (a) \( \sin(10^{\circ}) \) and (b) \( \cos(80^{\circ}) \) is dependant on the calculator in use. After performing the calculations with the correct mode and rounding to four decimal places, the results will be found.

Step by step solution

01

Check the Calculator Mode

Make sure your calculator is set to 'degree' mode since the values given are in degrees. If it is in 'radian' mode, switch it to 'degree' mode.
02

Calculate \( \sin(10^{\circ}) \)

Input 'sin 10' into your calculator and press 'Equals' for the result. Remember to round the answer to four decimal places.
03

Calculate \( \cos(80^{\circ}) \)

Input 'cos 80' into your calculator and hit 'Equals' for the result. Remember to round the answer to four decimal places.

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Most popular questions from this chapter

The numbers of hours \(H\) of daylight in Denver, Colorado, on the 15 th of each month are: \(1(9.67), 2(10.72), \quad 3(11.92), \quad 4(13.25)\) \(5(14.37), \quad 6(14.97), \quad 7(14.72), \quad 8(13.77), \quad 9(12.48)\) \(10(11.18), \quad 11(10.00), \quad 12(9.38) . \quad\) The month is represented by \(t,\) with \(t=1\) corresponding to January. A model for the data is \(H(t)=12.13+2.77 \sin \left(\frac{\pi t}{6}-1.60\right)\) (a) Use a graphing utility to graph the data points and the model in the same viewing window. (b) What is the period of the model? Is it what you expected? Explain. (c) What is the amplitude of the model? What does it represent in the context of the problem? Explain.

Angle of Elevation The height of an outdoor basketball backboard is \(12 \frac{1}{2}\) feet, and the backboard casts a shadow \(17 \frac{1}{3}\) feet long. A. Draw a right triangle that gives a visual representation of the problem. Label the known and unknown quantities. B. Use a trigonometric function to write an equation involving the unknown angle of elevation. C. Find the angle of elevation of the sun.

Write the function in terms of the sine function by using the identity $$A \cos \omega t+B \sin \omega t=\sqrt{A^{2}+B^{2}} \sin \left(\omega t+\arctan \frac{A}{B}\right).$$ Use a graphing utility to graph both forms of the function. What does the graph imply? $$f(t)=4 \cos \pi t+3 \sin \pi t$$

Use a graphing utility to graph the function and the damping factor of the function in the same viewing window. Describe the behavior of the function as \(x\) increases without bound. $$h(x)=x \sin \frac{1}{x}$$

Write the function in terms of the sine function by using the identity $$A \cos \omega t+B \sin \omega t=\sqrt{A^{2}+B^{2}} \sin \left(\omega t+\arctan \frac{A}{B}\right).$$ Use a graphing utility to graph both forms of the function. What does the graph imply? $$f(t)=3 \cos 2 t+3 \sin 2 t$$
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