Find Amplitude, Period, and Phase Shift y=sin(x)+8

Problem

y equals sine x plus 8

Solution

1. Identify the standard form of the trigonometric function, which is y equals A the sine of open paren B times open paren x minus C close paren close paren plus D

2. Determine the amplitude by looking at the coefficient A in front of the sine function. Here, A equals 1

3. Calculate the period using the formula P equals the fraction with numerator 2 pi and denominator the absolute value of B Since the coefficient of x is B equals 1 the period is 2 pi

4. Find the phase shift by identifying the value of C Since there is no horizontal shift inside the sine function, C equals 0

5. Note that the constant D equals 8 represents a vertical shift, which does not affect amplitude, period, or phase shift.

Final Answer

Amplitude equals 1 comma Period equals 2 pi comma Phase Shift equals 0

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