All Trigonometry Resources
Example Question #3 : Trigonometric Graphs
Identify the phase shift of the following equation.
If we use the standard form of a sine function
the phase shift can be calculated by . Therefore, in our case, our phase shift is
Example Question #4 : Trigonometric Graphs
Which of the following is equivalent to
The first zero can be found by plugging 3π/2 for x, and noting that it is a double period function, the zeros are every π/2, count three back and there is a zero at zero, going down.
A more succinct form for this answer is but that was not one of the options, so a shifted cosine must be the answer.
The first positive peak is at π/4 at -1, so the cosine function will be shifted π/4 to the right and multiplied by -1. The period and amplitude still 2, so the answer becomes .
To check, plug in π/4 for x and it will come out to -2.