SEND - IN ASSIGNMENT Page 1 of 8 REVIEW ASSIGNMENT PERIODIC and SINUSOIDAL FUNCTIONS Total ______ = _________% Name: _________________________________________...

Math 12 pages 4-8


SEND - IN ASSIGNMENT Page 1 of 8 REVIEW ASSIGNMENT PERIODIC and SINUSOIDAL FUNCTIONS Total ______ = _________% Name: _________________________________________ Teacher:________________________________________ School:_________________________________________ 63 Page 2 of 8 All answers rounded to 2 decimal places unless otherwise stated. Show all work. 1. Convert 220° to radians. Express the angle to 2 decimal places. 1. _____________________________ 1 mark 2. Estimate the value of 75° in radians. 2. _____________________________ 2 marks 3. Estimate the value of 6.5 radians in degrees. Answer to the nearest degree. 3. _____________________________ 2 marks 4. Convert 5 16 π radians to degrees. Answer to the nearest degree. 4. _____________________________ 1 mark 5. A circle has a radius of 12 cm. Calculate the length of arc a subtended by an angle of 140° . 5. _____________________________ 2 marks a 12 cm 140° Page 3 of 8 6. On the grid provided draw the angle 215 in Standard Position. Determine an angle that is negative co-terminal to 215 1 mark 6) co-terminal ___________________ 1 mark 7. Determine the period of each function: a) 2sin 7 y xπ= a) _____________________________ 1 mark b) cos 2( 45 )y x= −  b) _____________________________ 1 mark c) 1cos ( 90 ) 4 y x= +  c) _____________________________ 2 marks Page 4 of 8 8. Determine the domain and range of the function: ( )34cos 1 3 2 y x= − − + Domain: _____________________________ 1 mark Range: _____________________________ 1 mark 9. Given the function: ( )3sin 4 60 4y x= − + − , determine the amplitude, period, phase shift (indicate which direction for phase shift), and vertical displacement. Amplitude: ___________________ 1 mark period: ___________________ 1 mark phase shift: ____________________ 2 marks vertical displacement: ____________________ 1 mark 10. Given the function 26cos 2 14 y xπ= − . a) Find the period of the function b) Write the equation of the midline a) _____________________________ 1 mark b) _____________________________ 1 mark Page 5 of 8 11. Find the equation of a positive cosine function graphed below with the smallest phase shift right. 11. _____________________________ 4 marks 12. Write a negative sine function for the graph below. Start with a phase shift to the left. 12. _____________________________ 4 marks Page 6 of 8 13. Graph at least 2 periods for each function on the grid provided. a) sin 2 4 2 y x π = − + +    4 marks b) ( )4cos3 45y x= −  4 marks y 2 π − π 2π y 45° 90° 135° 180° Page 7 of 8 14. The high tide in a harbor occurs at 2:30 am and the depth at high tide is 16 meters. 8.4 hours later the low tide occurs. The depth of low tide is 4 meters. The equation of the function is ( )2 2 5( ) 6cos 10 16 8 t h t π − = + . . where h(t) is the height of the water, t hours after midnight. Time is represented as a decimal [2.5 is two and one half hours after midnight, so 2:30 am] Show the graph of this function in an appropriate window on the TI84 calculator for a 24 hour day. At what time will the depth of the water be 14 meters for the second time after midnight? What will the depth of the water be at 8:15 am? Time water is 14 m for 2nd time after midnight: ___________ 1 mark