Topic 11 - Shapes

Question 1

How do you find the area of a circle?

Answer 1

∏ x r(root 2)

Question 2

How do you find the area of the circumference of a circle?

Answer 2

∏ x Diameter

Question 3

How do you find the arc length of a circle?

Answer 3

Angle
——– x ∏ x D
360

Question 4

How do you find the area of a sector of a circle?

Answer 4

Angle
——– x ∏ x r(root 2)
360

Question 5

What side of a triangle is always the diagonal line?

Answer 5

Hypotenuse

Question 6

What is the equation for Pythagoras Theorem?

Answer 6

a(root 2) + b(root 2) = c(root 2)

Question 7

When finding:
The long side
The short side
in Pythagoras Theorem, what do you do?

Answer 7

+

-

Question 8

How do you do trigonometry?
e.g. angle ABC = 50
length AB = 10
Find length BC

Answer 8

Soh Cah Toa

Cos x = a/h
Cos 50 = a/10
Cos 50 x 10 = a
BC = 6.4

Question 9

How do you always find the largest angle in a triangle?

Answer 9

Opposite the longest side

Question 10

What do you always have for Cosine Rule, Sine rule and the area of a non-right angled triangle?
What do you want?

Answer 10

3 features

4 features

Question 11

When do you use the Cosine Rule?

Answer 11

When you have:
Two sides
One angle

With the angle in-between the two sides ‘cosy angle’ and are trying to find the length opposite the ‘cosy angle’

Question 12

When do you use the Sine Rule?

Answer 12

When you have:
One side
Two angles

When one side is opposite one angle and you are trying to find the side opposite the other angle.

Question 13

When using the Sine Rule, what do you do to find:
The angle
The length

Answer 13

Sin A/ a = Sin B/ b, than inverse sin

a/ Sin A = b/ Sin B

Question 14

Sine Graph:
What size is the cycle?
What is the first step to get x?
What is the second step once you get x?
How many solutions to you get per cycle?
e.g. Sin x = 0.5 in the range 0 to 360

Answer 14

0 degrees to 360 degrees

Inverse sin (x) = y

If y is positive:
180 - y
If y is negative:
180 + y = a
540 + a  

2 solutions per 360 degrees

e.g. Inverse sin (0.5) = 30
180 - 30 = 150
x = 30, x = 150

Question 15

Cosine Graph:
What size is the cycle?
What is the first step to get x?
What is the second step once you get x?
How many solutions to you get per cycle?
e.g. Cos x = 0.5 in the range 0 to 360

Answer 15

0 degrees to 360 degrees

Inverse cos (x) = y

If y is positive or negative:
360 - y

2 solutions per 360 degrees

e.g. Inverse cos (0.5) = 60
360 - 60 = 300
x = 60, x = 300

Question 16

Tan Graph:
What size is the cycle?
What is the first step to get x?
What is the second step once you get x?
How many solutions to you get per cycle?
e.g. Tan x = 0.5 in the range 0 to 360

Answer 16

0 degrees to 180 degrees

Inverse tan (x) = y

If y is positive:
180 + y
If y is negative:
180 + y = a
a + 180 

2 solutions per 180 degrees

e.g. Inverse tan (0.5) = 26.565
180 + 26.565 = 206.565
1) x = 26.6, x = 206.6
(because the above is only for 0 to 180, you have to add 180 to both x values to get the 3rd and 4th solutions)
26.6 + 180 = 206.6
206.6 + 180 = 386.6
x = 26.6, x = 206.6, x = 206.6, x = 386.6