Suppose g(a) = 0.35 sin(22a - 13) a. What is the argument of the sine function?

Question

Suppose g(a) = 0.35 sin(22a - 13) a. What is the argument of the sine function? (Enter an expression.) b. The argument of the sine function represents what quantity? angle measure (in radians) vertical distance above the horizontal diameter (measured in radius lengths) horizontal distance to the right of the vertical diameter (measured in radius lengths) radius length number of seconds elapsed c. For the value of sine to vary through a complete cycle of its outputs, the value of the argument must increase from 0 to d. For the value of 22a - 13 = 0, the value of a must equal e. For the value of 22a - 13 = 2pi the value of a must equal f. For the value of sine to vary through a complete cycle of its outputs, the value of the input of g must vary by g. What is the period of the function g?

Explanation / Answer

g(a) = 0.35sin(22a - 13)

a) Argument = 22a -13

b) angle in radians

c) Period of the function g(a) = 2pi/22 = pi/11

So, 22a -13 =0 ; a = 13/22

period = pi/11 ; a = 13/22 + pi/11 = 14pi/22 = 7pi/11

argument at a= 7pi/11 ; argument = 22(7pi/11) - 13 =14 - 13 = 1

So, argument should vary from 0 to 2pi

d) 22a -13; a = 13/22

e) 22a - 13 = 2pi ; 22a = 2pi +13

a = (2pi +13)/22

f) Over a cycle g would vary from 0.35 to 0.35 ie.e 0 units

g) period = pi/11

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