Grade 12 Trigonometric functions practice questions with answers

MASALALM MATHEMATICS TRIG FUNCTION PRACTICE QUESTIONS


Exam PRACTICE Questions: Trigonometric functions
Question 1:
The graphs of f(x) = a sin(bx) + 1 and g(x) = 2 cos(x + p) are shown for -90° ≤ x ≤ 180°.




A (-30; m)




B (48; k)




1.1 Write down the amplitude of g.
1.2 Determine the period of f.
1.3 Determine the values of a, b, and p.
1.4 Determine the value(s) of x such that:
1.4.1 g(x) > 0
1.4.2 f(x) = g(x)
1.4.3 f(x) g(x) < 0
1.5 Describe the transformations applied to the graph of 2cosx to obtain the graph
g(x)=2cos(x+30)

,1.6 The graph of g(x) is shifted 60° to the left to form the graph of h(x). Determine the equation
of h(x) in its simplest form.
1.7 Write down the maximum value of g(x) − 2.

Question 2:
The graphs of f(x) = 3 sin(2x) - 1 and g(x) = cos(x) are shown for [-180° ; 180°].
Given co-ordinates A(20; m) and B(78; k)


h



A
B


g




f

2.1 Write down the amplitude of g.
2.2 Determine the period of f.
2.3 Determine the values of a, b, and p.
2.4 Determine the value(s) of x such that:
2.4.1 g(x) > 0 for the domain −180<x<180
2.4.2 f(x) = g(x) for the domain 0<x<180
2.4.3 f(x) g(x) <0 for the domain 45<x<180
2.4.4 f(x)−g(x)>0 for the domain 0<x<180
2.4.5 g(x)−f(x)>0 for the domain 0<x<180
2.5 The graph of f(x) is shifted 1 unit upward to form the graph of h(x). Determine the value(s)
of x such that for the domain −180<x<180:
2.5.1 g(x) = h(x)

, 2.5.2 h(x)−g(x) < 0
2.5.2 g(x)−h(x) < 0
2.5.3 h(x) g(x) <0



Question 3:
The graphs of f(x) = a sin (bx) and g(x) = −3 cos(x + p) are shown for [-360°; 360°].




45




3.1 Write down the amplitude of g.
3.2 Determine the period of f.
3.3 Determine the values of a, b, and p.
3.4 Determine the value(s) of x such that:
3.4.1 g(x) > 0
3.4.2 f(x) g(x) <0
3.5 If h(x)= cos2x and f(x) =4sinx, determine the maximum value of h(x) −f(x) on the interval
[0°; 360°]