Trigonometric Graphs (Grade 10) — Worksheet & Memo

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Grade 10 · Trigonometry

Trigonometric Graphs (Grade 10)

MEMORANDUM

Name:

Class:

Date:

Mark

/ 21

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
Write down the amplitude of y = 2 sin x.
(1)
2✓ (1)
2
Write down the period of y = sin x.
(1)
360°✓ (1)
3
Write down the range of y = 2 sin x + 1.
(2)
−1 ≤ y ≤ 3✓✓ (2)
4
Describe the transformation from y = cos x to y = cos x + 1.
(2)
A shift of 1 unit upwards✓✓ (2)
5
Write down the equations of the asymptotes of y = tan x for x ∈ [0° ; 360°].
(2)
x = 90° and x = 270°✓✓ (2)
6
Write down the maximum value of y = 3 cos x − 1.
(2)
3 − 1 = 2✓✓ (2)
7
For what value of x in [0° ; 360°] does y = sin x reach its minimum?
(1)
x = 270°✓ (1)
8
What does a negative value of a do to y = a sin x?
(1)
It reflects the graph in the x-axis.✓ (1)
9
The graph of y = a sinθ + q, where a > 0, has a maximum value of 7 and a minimum value of 1. Determine the values of a and q, and write down the equation of the graph.
(3)
q = (7 + 1)/2 = 4 ✓; a = (7 − 1)/2 = 3 ✓; y = 3 sinθ + 4 ✓(3)
10
The graph of y = a cosθ + q, where a > 0, has a range of [−5 ; 3]. Determine a and q.
(3)
q = (3 + (−5))/2 = −1 ✓; a = (3 − (−5))/2 = 4 ✓; so y = 4 cosθ − 1 ✓(3)
11
A cosine graph passes through a MINIMUM at θ = 0° and has amplitude 2 with no vertical shift. Write down its equation and explain the sign of a.
(3)
y = −2 cosθ ✓✓; a is negative because an ordinary cosine graph starts at a maximum — starting at a minimum means it has been reflected in the θ-axis ✓(3)

TOTAL: 21 marks