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

Answer 1

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.

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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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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