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Reading a Phase Shift

Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 26 of 49.

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∘)y = 2\sin\left(x-90^{\circ}\right). The same curve is −2 cos x, but the form asked for decides how you write it.

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Challenge

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

Try it yourself

Write the equation of the graph

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