1. cos 75 2. sin (-210") 3. sin 4. cos 177 12 12 5. tan 12 6. tan 12 7. VOLTAGE Analysis of the voltage in a hairdryer involves terms of the form sin (wwof - 90 ), where it is a positive integer, to is the frequency of the voltage, and f is time. Use an identity to simplify this expression. (Example 2) 3. BROADCASTING When the sum of the amplitudes of two waves is greater than that of the component waves, the result is constructive interference. When the component waves combine to have a smaller amplitude, destructive interference occurs. Constructive Interference Destructive Interference AA Consider two signals modeled by y = 10 sin (21 + 30") and y = 10 sin (21 + 210"). (Example 2) a. Find the sum of the two functions. b. What type of interference results when the signals modeled by the two equations are combined? 9. WEATHER The monthly high temperatures for Minneapolis can be modeled by /(x) = 31.65 sin (#x - 2.09) + 52.35, where a represents the months in which January = 1, February = 2, and so on. The monthly low temperatures for Minneapolis can be modeled by g(x) = 31.65 sin (#x - 2.09) + 32.95. (Example 2) a. Write a new function h(x) by adding the two functions and dividing the result by 2. b. What does the function you wrote in part a represent? 10. TECHNOLOGY A blind mobility aid uses the same idea as a bal's sonar to enable people who are visually impaired to detect objects around them. The sound wave emitted by the device for a certain patient can be modeled by b = 30 (sin 195")4, where f is time in seconds and b is air pressure in pascals. (Example 2) a. Rewrite the formula in terms of the difference of two angle measures. b. What is the pressure after 1 second