MCF3M – Test #6: Trigonometric Functions



MHF4U – Test: Trigonometric Functions v2

Name: _______________________________ Mark: [pic] [pic] [pic]

KU APP TIPS

1. a) Determine the exact values of sec [pic]and tan [pic] (as a fraction), if [pic] is a quadrant 2 angle and the point [pic]is exactly 25 units from the origin and lies on the terminal arm of [pic].

[TIPS / 3]

b) Determine the value of [pic] in radians rounded to the nearest hundredth. [APP / 2]

2. Determine the arc length needed to construct an angle of 1.46 radians on a circle with a radius equal to 4.5 cm? [APP/2]

3. If [pic]is coterminal to[pic]. Determine the principal angle in radian measure. (Note: express as a fraction of [pic]) [KU3]

4. Determine two angles (one positive, one negative) that are coterminal to each of the following. (Note: express in same units as original) [KU4]

A) [pic] B) [pic]

5. Evaluate each of the following using special triangles. (Note: NO DECIMALS ALLOWED, simplify fully for full marks) [A / 4]

A) [pic] B) [pic]

7. Determine the value(s) of [pic] for each of the following. Consider [pic]. [APP / 6]

A) [pic] B) [pic]

8. Determine each of the following for the following function. [pic]

[KU / 4]

Amp: Period: Phase Shift: Vert. Shift:

9. A) Sketch and fully label one cycle of both functions[pic] and [pic]on the graph below. [A5]

| | | | | | |

|Y |-2 |1 |4 |1 |-2 |

10. A carnival Ferris wheel with a radius of 9.5 m rotates once every 22 seconds. The bottom of the wheel is located 1.5 m above the ground.

A) Determine the equation of the function that represents a rider’s height above the ground, in metres as a function of time, in seconds if the rider starts at a point 11 m above the ground and initially moves in an downward direction. [4]

B) Determine the height of the rider exactly 1 minute into the ride. Is the rider rising or falling at this point in time? [2]

C) Riders can see Niagara Falls if they are higher than 19 m above the ground. Determine the time intervals within the first 60 seconds that the rider can see the Falls. (This is tricky!!! Caution: CAST Rule!)[4]

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