Mathematics 30 June 1999 Grade 12 Diploma Exam

10. A student is investigating the effects of changing the values of the parameters
a, b, c, and d in the equation y = a sin[b(θ + c)] + d. The graph of each of the
following functions is plotted:
f (θ )=sinθ
g(θ) = 2 sinθ
h(θ )=sin2θ
k(θ)=sin(θ + 2)
l(θ )=sinθ + 2
The equation whose graph will have the same θ -intercepts as the graph
of y = f (θ ) is
A. y = g(θ )
B. y = h(θ )
C. y = k(θ )
D. y = l(θ )
11.
⎛3θ⎞
⎛θ 3θ θ
An equivalent expression for cos⎜
2
⎟ cos⎜ 2
sin
2
sin
⎝ ⎠ ⎝ ⎠ ⎟ + ⎛ ⎞ ⎛
⎜ ⎟ ⎜ ⎞ ⎝ ⎠ ⎝2⎠ A. sin(2θ )
B. cos(2θ )
C. sin(θ )
D. cos(θ )
12. An equivalent expression for
A. sin 2 x
B. sin x
C. cos 2 x
D. cos x
(sin x)(cos
x)
tan x
is
6