Question

assignment 8.2: graphs of the other trigonometric functions
score: 0/32 answered: 0/8
question 1
given the equation ( y = 8\tan(6x - 24) )
the period is:
the horizontal shift is: units to the
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Explanation:

Step1: Recall the formula for the period of \(y = A\tan(Bx - C)\)

The period of \(y = A\tan(Bx - C)\) is \(\frac{\pi}{|B|}\). In the given equation \(y = 8\tan(6x - 24)\), \(B = 6\).
So, the period is \(\frac{\pi}{6}\).

Step2: Recall the formula for the horizontal shift of \(y = A\tan(Bx - C)\)

The horizontal shift of \(y = A\tan(Bx - C)\) is \(\frac{C}{B}\) (to the right if \(C>0\)). In the given equation \(y = 8\tan(6x - 24)\), \(C = 24\) and \(B = 6\).
So, the horizontal shift is \(\frac{24}{6}=4\) units to the right.

Answer:

The period is \(\frac{\pi}{6}\).
The horizontal shift is \(4\) units to the right.