
Circular functions revision
Presentation
•
Mathematics
•
11th - 12th Grade
•
Medium
Sophie Bark
Used 5+ times
FREE Resource
16 Slides • 15 Questions
1
by Sophie Bark
2
The unit circle is the starting point for your revision...
3
4
Example -
Find the value of
a)
b)
c)
5
Example -
Find the value of...
b)
c)
6
Multiple Choice
Which other angle gives the same value as sin4π ?
43π
45π
47π
411π
7
Multiple Choice
If sinθ=0.68 , find the value of sin(π+θ)
0.68
-0.68
0.32
-0.32
8
Multiple Choice
If tanx=tan(6π) , π≤x≤2π , find x
x=6π
x=65π
x=67π
x=611π
9
Multiple Choice
What is the length of the arc on the unit circle between 0° and 90° ?
π cm
2π cm
2π cm
4π cm
10
Multiple Choice
What is the length of an arc formed by an angle of 60° in a circle with radius 8cm?
38πcm
332πcm
3πcm
6πcm
11
The test is going to be CAS active, but you may need to show working out for some questions.
We will practise the CAS skills first!!
12
13
14
Fill in the Blanks
These values of x would be the
Type answer...
15
Open Ended
What is the amplitude and period of the graph y=2sin(2x)−1
16
The amplitude is the distance from the mean (middle) of the graph to the maximum of minimum.
The period is how long it takes for the graph to make one complete cycle.
17
Multiple Choice
What is the range of y=2sin(2x)−1
[−2,2]
[−1,1]
[−1,3]
[−3,1]
18
Multiple Choice
Which is the correct sketch of y=2sin(2x)−1 ?
19
20
Multiple Choice
Solve the equation finding all solutions
2cos(3x)−3=0 , x∈[0,2π]
x=18π,1811π,1813π, 1823π, 1825π,1835π
x=18π, 1811π
x= 18π, 1811π, 1813π, 1823π, 1825π, 1835π,1837π,1847π
x=18π, 1811π, 1823π, 1835π
21
Multiple Choice
What is the smallest value of f(x)=5−sinx
If using CAS, you must include a domain (hint: one complete cycle will contain 1 minimum & 1 maximum)
−1
4
−5
−4
22
23
24
25
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Open Ended
State the sequence of transformations that takes y=tanx to y=−tan(3x)−5
27
Dilation by factor 1/3 from y-axis
Reflection in the x-axis
Translation 5 units in the negative direction of y-axis
28
Open Ended
State the sequence of transformations that takes y=cosx to y=3cos(21(x−4π))+7
29
1. Translation pi/4 units in the positive direction of the x-axis (right)
2. Dilation by factor 2 from the y-axis
3. Dilation by factor 3 from the x-axis
4. Translation 7 units in the positive direction of y-axis (up)
30
Poll
How confident do you feel with circular functions?
Very confident with all aspects
Confident with the concepts, but I need to practise
I understand most things, but I need to practise. There are still one or two things I don't understand.
I understand about half, and there is half that I don't understand.
I don't understand most of it
31
Open Ended
What do you need the most help with? Please try and be specific here, e.g.
I can solve, but I struggle to find all solutions in the domain..
I find it hard to sketch when there is a vertical translation
I don't understand the difference between the amplitude and the range
etc
by Sophie Bark
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