Reading a Phase Shift

Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 28 of 51.

To read y = a sin(x − h), with a positive, off a graph, find the amplitude from the top, then find a place where the wave crosses its middle going up: that x is h. A wave has one such crossing every period, so pick the first one at or to the right of 0 and the answer is unique.

$A sine wave of amplitude 2 crossing going up at 90 degrees$

This wave tops out at 2 and crosses going up at 90°, so it is y = 2sin(x - 90°). The same curve is −2 cos x, but the form asked for decides how you write it.

Challenge

Write the equation of the wave in the graph tile in the form y = a×sin(x - h), with a positive and h in degrees from 0° to 360°, written with the ° sign. Press Check.