84
Trigonometric functions
8.4.1 (a) On the same set of axes, sketch the graphs of f(x)=sin(x-60°) and g(x)= cos 2x
for the interval -180°≤x≤180°. Indicate clearly the intercepts with the axes and the
turning points.
(b) Write down the range of f
(c) Write down the period of g.
(6) L2
(1) LI
(1) LI
= cos 2.x.
(5) L3
(e) Hence, for which values of x in the interval -180° (f) If p(x)=-cos(2x+20°), describe fully, in words, the transformation from g to p.
(3) L2
(3) L3
(d) Determine the general solution of sin (x-60°)= co
8.4.2 Consider the functions defined by f(x)=sin 2x and g(x)=cos(x+60°).
(a) Draw a neat sketch of the curves of fand g for -180° the intercepts with the axes.
(b) Write down the range for g.
(c) Write down the period of f
(d) For which value(s) of x is the graph of g decreasing?
(6) L2
(1) LI
(1) L1
(2) L2
8.4.3 In the diagram below the graphs of g(x)=sin(x + a) and h(x)=b tan cx are drawn in the interval
IE[-180°; 180°]. g and h intersect at D(-135°; -1) and E(-22,3°; 0,4).
y
1,5
h
五
​