Game Maths

Question 1

A radian is equivalent to approx how many degrees?

Answer 1

57.2958 degrees

Question 2

How many radians in a circle?

Answer 2

6.2832

Question 3

In pi - what does 360 degrees equal?

Answer 3

2 PI

Question 4

in pi - what does 180 degrees equal?

Answer 4

PI

Question 5

In pi - what does 90 degrees equal?

Answer 5

PI / 2

Question 6

What is a JavaScript formula for converting degrees to radians?

Answer 6

radians = degrees * Math.PI / 180;

Question 7

What is a JavaScript formula for converting radians to degrees?

Answer 7

degrees = radians * 180 / Math.PI;

Question 8

The opposite side to an angle…

Answer 8

does not touch the angle

Question 9

The adjacent side to an angle…

Answer 9

touches the angle (and is not the hypotenuse)

Question 10

The sine of an angle is…

Answer 10

the ratio of the lengths of the side opposite the angle and the hypotenuse

opposite side / hypotenuse

Question 11

When you use Math.sin, the result may not be what you expect - what step do you have to make to make this make sense?

Answer 11

convert the angle to radians

Question 12

What do you need to remember about angles in JavaScript?

Answer 12

The coordinate system is reversed due to the origin being in the top / left corner. So the positive direction is clockwise, rather than counter-clockwise as in standard maths.

0 Degrees is still in the positive X direction though.

Question 13

What is the cosine of an angle defined as?

Answer 13

Ratio of the adjacent leg of an angle to the Hypotenuse

adjacent leg / hypotenuse

Question 14

You need to find out the cosine of an angle 30 degrees - how would you do that?

Answer 14

Math.cos(30 * Math.PI / 180)

NOTE: We have to convert to radians first!

Question 15

You need to find out the sine of an angle 30 degrees, how would you do that?

Answer 15

Math.sin(30 * Math.PI / 180)

NOTE: We have to convert to radians first!

Question 16

In a triangle, the cosine of one angle is the…

Answer 16

sine of the other angle

Question 17

The tangent of an angle is the ratio of…

Answer 17

the opposite leg and the adjacent leg

opposite leg / adjacent leg

Question 18

What does Math.asin do?

Answer 18

It’s the arcsine - it does the reverse of sin.

Pass in an ratio and it will give you the angle.

Question 19

How would you determine the angle given an opposite leg and a hypotenuse of 1 and 2?

Answer 19

Math.asin(1 / 2) * 180 / Math.PI;
Gives 30 (or 29.999);

Question 20

How would you determine the angle given an adjacent leg and hypotenuse of 1.73 and 2?

Answer 20

Math.acos(1.73 / 2) * 180 / Math.PI;
Gives 30 (or 29.999)

Question 21

What does Math.atan do?

Answer 21

It’s the arctangent - it does the reverse of tangent

Pass in the ratio and it will give you the angle

Question 22

How would you determine the angle given the opposite leg and adjacent leg of -1 and 1.73?

Answer 22

Math.atan(-1 / 1.73) * 180 / Math.PI

Question 23

What is the downside to using Math.atan?

Answer 23

If you ratios of -1 and -2, or 1 and 2 - they will give you the same ratio 0.5. So it’s not possible to determine which triangle the result will be refering too.

Question 24

What is Math.atan2(y, x)?

Answer 24

It’s like Math.atan - however, it takes the measurement of the opposite side, and the adjacent side as separate parameters.

Question 25

What is the sine of 0?

Answer 25

0

Question 26

What does a sign wave represent?

Answer 26

The values of sine for all the angles from 0 to 360

Question 27

What are the two main coordinate systems?

Answer 27

Polar and Cartesian

Question 28

How would you find the polar coordinates given an x and y coordinate, around a central position?

Answer 28

var originx = 100;
var originy = 100;
var positionx = 150;
var positiony = 150;
radians = Math.atan2(positiony - originy, positionx - originx);

Question 29

What do you have to keep in mind with results from atan2?

Answer 29

The range is between [-π, π] - which means you don’t know the 360 value. To change this, (assuming radians)…

if (angle