QUESTION 1 a) Solve the equation (sin B) 2 -3sin B + 2 = 0 where 0 B 2. b) Show

Question

QUESTION 1

a) Solve the equation (sin B)2 -3sin B + 2 = 0 where 0 B 2.
b) Show that cos3B+cosB=2(cos2B)cos B.
c) On the same axes, sketch the graphs of y = sin A and y = cos A for 0 A . Hence, find all the intersection points(if any) of the two graphs.

QUESTION 2

The functions f and g are defined as
f : x+3
and g : x x+1
a) Obtain the domains and ranges of f and g.
b) Obtain the function of f o g and the value of f o g (1).
c) Obtain the function of g o f and the value of g o f (1).
d) Sketch the graphs of f, g, f o g and g o f on the same axes

Explanation / Answer

Solve the equation (sin B)2 -3sin B + 2 = 0 where 0 B 2

(sin B)2 - 2sin B - sin B +2 = 0

sin B (sin B -2) -1 (sin B -2) = 0

(sin b - 2) (sin b -1) = 0

sin b = 2 or sin b =1

b = sin^-1 B or b = 90*

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