Circular functions revision

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Mathematics

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11th - 12th Grade

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Sophie Bark

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16 Slides • 15 Questions

Circular functions revision

by Sophie Bark

The unit circle

The unit circle is the starting point for your revision...

The unit circle

Finding angles in different quadrants

Example -

Find the value of

Finding angles in different quadrants

Example -

Find the value of...

Multiple Choice

Which other angle gives the same value as $\sin\frac{\pi}{4}$ ?

$\frac{3\pi}{4}$

$\frac{5\pi}{4}$

$\frac{7\pi}{4}$

$\frac{11\pi}{4}$

Multiple Choice

If $\sin\theta=0.68$ , find the value of $\sin\left(\pi+\theta\right)$

0.68

-0.68

0.32

-0.32

Multiple Choice

If $\tan x=\tan\left(\frac{\pi}{6}\right)\ ,\ \pi\le x\le2\pi$ , find $x$

$x=\frac{\pi}{6}$

$x=\frac{5\pi}{6}$

$x=\frac{7\pi}{6}$

$x=\frac{11\pi}{6}$

Multiple Choice

What is the length of the arc on the unit circle between $0\degree$ and $90\degree$ ?

$\pi$ cm

$\ 2\pi$ cm

$\frac{\pi}{2}$ cm

$\frac{\pi}{4}$ cm

Multiple Choice

What is the length of an arc formed by an angle of $60\degree$ in a circle with radius 8cm?

$\frac{8\pi}{3}cm$

$\frac{32\pi}{3}cm$

$\frac{\pi}{3}cm$

$\frac{\pi}{6}cm$

Solving Equations to find solutions in a specified domain

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!!

Solve the equation using CAS

Solve the equation using CAS - check your answer

Fill in the Blanks

Type answer...

Open Ended

What is the amplitude and period of the graph $y=2\sin\left(2x\right)-1$

Type response here

Amplitude and period

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.

Multiple Choice

What is the range of $y=2\sin\left(2x\right)-1$

$\left[-2,2\right]$

$\left[-1,1\right]$

$\left[-1,3\right]$

$\left[-3,1\right]$

Multiple Choice

Which is the correct sketch of $y=2\sin\left(2x\right)-1$ ?

Now for some CAS practise

Multiple Choice

Solve the equation finding all solutions

$2\cos\left(3x\right)-\sqrt{3}=0\ ,\ x\in\left[0,2\pi\right]$

$x=\frac{\pi}{18},\frac{11\pi}{18},\frac{13\pi}{18},\ \frac{23\pi}{18},\ \frac{25\pi}{18},\frac{35\pi}{18}$

$x=\frac{\pi}{18},\ \ \frac{11\pi}{18}$

$x=\ \frac{\pi}{18},\ \frac{11\pi}{18},\ \frac{13\pi}{18},\ \frac{23\pi}{18},\ \frac{25\pi}{18},\ \ \frac{35\pi}{18},\frac{37\pi}{18},\frac{47\pi}{18}$

$x=\frac{\pi}{18},\ \ \frac{11\pi}{18},\ \ \frac{23\pi}{18},\ \ \frac{35\pi}{18}$

Multiple Choice

What is the smallest value of $f\left(x\right)=5-\sin x$

If using CAS, you must include a domain (hint: one complete cycle will contain 1 minimum & 1 maximum)

$-1$

$4$

$-5$

$-4$

Sequences of Transformations

Open Ended

State the sequence of transformations that takes $y=\tan x$ to $y=-\tan\left(3x\right)-5$

Type response here

Dilation by factor 1/3 from y-axis

Reflection in the x-axis

Translation 5 units in the negative direction of y-axis

Open Ended

State the sequence of transformations that takes $y=\cos x$ to $y=3\cos\left(\frac{1}{2}\left(x-\frac{\pi}{4}\right)\right)+7$

Type response here

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)

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

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

Type response here

Circular functions revision

by Sophie Bark

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Circular functions revision

Circular functions revision

​The unit circle

​The unit circle

​Finding angles in different quadrants

​Finding angles in different quadrants

​Solving Equations to find solutions in a specified domain

​Solve the equation using CAS

​Solve the equation using CAS - check your answer

​Amplitude and period

​Now for some CAS practise

​Sequences of Transformations

​Sequences of Transformations

Circular functions revision

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

The unit circle

The unit circle

Finding angles in different quadrants

Finding angles in different quadrants

Solving Equations to find solutions in a specified domain

Solve the equation using CAS

Solve the equation using CAS - check your answer

Amplitude and period

Now for some CAS practise

Sequences of Transformations

Sequences of Transformations