How do you find the period, phase and vertical shift of y=1/2csc3(theta-45^circ)+1?

1 Answer
ChemCrazy
Nov 27, 2017

To find the period, look at k in the equation y=acsck(theta-d) +c
The phase and vertical shift are also right in the equation as d and c.

Explanation:

Period:
period=(2pi)/k

In the equation, look for k, which in this case, is 3.

So:
period= (2pi)/3

In degrees, it would be
180^o/(pi rad)=rad

=180^o/(pi rad) * (2pi)/3

=(180^o*3)/2

=270^o

Phase Shift:
The phase shift is also in the equation too, in which case you look for d. In this equation d is 45^o

Since it is a negative 45^o, it is then said that the graph moves 45^o to the left.

Vertical Shift:
The vertical shift is the last part of the equation: c, which is in this equation, 1 . If it is positive, it goes up. Negative shifts down. In this equation, the graph will shift up 1 unit.

Please correct me if I am wrong!

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