Grade 12 trigonometric graphs exam practice part 1
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Course
Mathematics
Institution
12th Grade
This document is designed for Grade 12 students preparing for their trigonometric functions exam. It provides a series of challenging and insightful practice questions focused on understanding and analyzing trigonometric graphs. Perfect for exam preparation, this resource ensures students are well-...
MATHEMATICS TRIG FUNCTIONS part 1
GRADE 12 TRIGONOMETRIC FUNCTION EXAM PRACTICE
Question 1
Consider the graph of f(x) = cos x + 1 for [ −90° ;270°]
1.1 Write down the range and period of f.
1.2 Describe the transformations applied to the basic graph of cosx to obtain the graph f(x)=cosx+1
1.3 Show that cos x + 1 = sin (2x+90°) can be rewritten as (2 cos x + 1) cos x = 0.
1.4 Hence, or otherwise, determine the general solution of cos x + 1 = sin (2x+90°).
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,1.5 Describe the transformations applied to the basic graph of sinx to obtain the graph of
g(x) =2sin (2x+30°).
1.6 For the functions f(x) =cosx+1 and g(x) =2sin (2x+30), determine the maximum value of
f(x) −g(x) on the interval [−90°; 180°]
1.7 For the functions f(x)=cosx+1 and h(x)=−cos(2x), determine the maximum value of f(x)−h(x)
on the interval [−90°;180°].
Question 2
In the diagram below, the graph of ƒ (x) = − sin x is drawn for −180° ≤ x ≤ 180°.
3.1 Draw the graph of g(x) = cos(x+30°) for x= [−180°; 180°] on the grid provided in the
ANSWER BOOK.
3.2 Determine the values of x in the interval x= (−180°; 180°) for which cos(x+30°) − sin x > 0.
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, Question 4
The graph of f(x) = 3 sin x is drawn for the interval x= [0°; 360°].
4.1 Write down the amplitude of f(x).
4.2 Determine the period of g(x) =sin (2x − 45°).
4.3 Determine the values of x in the interval x= [0°; 360°] for which 3 sin a cos(2x − 45°).
Question 5
In the diagram, the graphs of the functions f(x) = sin x + 2 and g(x) = tan(x + 45°) are drawn for
the interval 0° ≤ x ≤ 180°.
5.1 Write down the range of f(x).
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