Math  /  Trigonometry

QuestionNATIONAL 5 MATHS 2014 126
10. The graph of y=asin(x+b),0x360y=a \sin (x+b)^{\circ}, 0 \leq x \leq 360, is shown below.

Write down the values of aa and bb.

Studdy Solution
To find the horizontal shift b b , observe the phase shift of the sine function.
The standard sine function y=asin(x) y = a \sin(x) has a maximum at x=90 x = 90^\circ .
In the given graph, the maximum occurs at x=90b x = 90^\circ - b .
Since the maximum is observed at x=0 x = 0^\circ , we have:
90b=0 90^\circ - b = 0^\circ
Solve for b b :
b=90 b = 90^\circ
The values of a a and b b are:
a=3 a = 3
b=90 b = 90^\circ

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