Functions (MCR3U) · Trigonometric Functions

Transformations of sine and cosine functions

Find the amplitude, period, or a specific value of a transformed sine or cosine function; at the highest difficulty this is framed as a real-world (Ferris wheel) problem. Unlimited questions, five difficulty levels, and a full worked solution every time — free.

Practice this skill Curriculum: MCR3U-TF2.1

Try one

State the amplitude of the function.

y = −2cos(3(x - 90)) + 3

Answer: 2

See one solved, step by step

For the function below, find y when x = 45.

y = 4cos(2(x - 45)) + 2
📘 Worked solution
1When x = 45, the inside becomes 2(x - 45) = 0degThis x-value was chosen to make the angle inside sin/cos a nice multiple of 90deg.
2y = 4·cos(0deg) + 2Substitute the angle into the function.
3cos(0deg) = 1, so y = 4·1 + 2 = 6Recall the value of cos at 0deg, 90deg, 180deg, and 270deg.

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