Exercise 10 Page 510

The shortest repeating portion of the graph of a sine or cosine function is called a cycle. The horizontal length of each cycle is the period. The reciprocal of the period is the frequency. Let's compare the given function with the general form of a transformed sine function. General Form y= a sin b(x- h)+ k [0.8em] Given Function y= 3 sin 0.2(x- 0)+ 6 The period of a sine function is 2π b. We can find the period of the given function by identifying the value of b. Period: 2π/b ⇒ 2π/0.2 Let's simplify this expression.

2π/0.2

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Simplify

WriteAsFrac

Write as a fraction

2π/210

DivByFracD

a/b/c= a * c/b

2π* 10/2

CancelCommonFac

Cancel out common factors

2π* 10/2

SimpQuot

Simplify quotient

π* 10/1

DivByOne

a/1=a

π * 10

Multiply

Multiply

10π

The period of the given function is 10π. As previously stated, the frequency is the reciprocal of the period. ccc Period & & Frequency [0.8em] 10π & ⇒ & 1/10π