Trigonometric Graphs (Grade 10) — Worksheet & Memo

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Grade 10 · Trigonometry

Trigonometric Graphs (Grade 10)

WORKSHEET

Name:

Class:

Date:

Mark

/ 21

Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

1
Write down the amplitude of y = 2 sin x.
(1)
2
Write down the period of y = sin x.
(1)
3
Write down the range of y = 2 sin x + 1.
(2)
4
Describe the transformation from y = cos x to y = cos x + 1.
(2)
5
Write down the equations of the asymptotes of y = tan x for x ∈ [0° ; 360°].
(2)
6
Write down the maximum value of y = 3 cos x − 1.
(2)
7
For what value of x in [0° ; 360°] does y = sin x reach its minimum?
(1)
8
What does a negative value of a do to y = a sin x?
(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)
10
The graph of y = a cosθ + q, where a > 0, has a range of [−5 ; 3]. Determine a and q.
(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)

TOTAL: 21 marks