sin equations, Math homework help

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1. Determine the angular velocity in radians per second of 4.3 revolutions in 5 seconds. Round the nearest tenth. Show work please 2. Find the area of a triangle with side lengths 17, 18, 21.4 units. Round the answer to the nearest hundredth. show work please 3. Explain how the transformations of the functions f(x) = sin (x+ pi/8) and g(x) = sin x + 8 differ. Show work please 4. Write the equation of the sine function with amplitude of 8.5, standard period,phase shift of 90 degrees and a vertical shift of 12. show work please 5. The temperature in your house is controlled by a thermostat. The temperature will vary according to the sinusoidal function f(x) = 7 sin (pi/12) (x-11)) + 33 where f(x) represents the temperature in degrees celsius and x is hours since midnight. What is the temperature of your house at midnight? a. 7 degrees celcius b. 16 degrees celcius c. 22 degrees celcius d. 31 degrees celcius 6. Given the vectors and Explain the difference between and (show work) 7. Given and find a. (1,0) b. (-7,4) c. (-12,-4) d. (-1, -4) 8. Give triangle ABC with a= 45 and b=5 and c=45 find angle B. Round the cosine value to the nearest thousandth and answer to the nearest hundredth a. 138 degrees b. 16 degrees c. 14 degrees d. 6 degrees 9. Given triangle ABC with a=10, b=16 and angle A= 30 degrees, determine both possible values for angle B a. 53 degrees, 127 degrees b. 53 degrees, 133 degrees c. 64 degrees, 127 degrees d. no solution. 10. Find the area of a sector of a circle if the central angle measures 90 degrees and the radius measures 4 degrees inches. a. 4 pi in^2 b. 18 pi in^2 c. 36 pi in ^2 d. 144 pi in ^2 11. Verify the following trig identity cotx/ cscx = cosx Show work. 12. Explain why there are restrictions on the domain for the function f(x)= 1/ x-7
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