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, included free with weekly lessons.
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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