Cast Diagrams

Question 1

Which trig function(s) are positive in the first quadrant and on what part of the diagram is this?

Answer 1

All of them and the top right.

Question 2

Which trig function(s) are positive in the second quadrant and on what part of the diagram is this?

Answer 2

sin and the top left.

Question 3

Which trig function(s) are positive in the third quadrant and on what part of the diagram is this?

Answer 3

tan and the bottom left.

Question 4

Which trig function(s) are positive in the fourth quadrant and on what part of the diagram is this?

Answer 4

cos and the bottom right.

Question 5

How do you use the cast diagrams to work out all possible values of x for sin, cos or tan x = y?

Answer 5

Find the corresponding sections of the cast diagram for whether y is positive or negative. From the horizontal, work out how many degrees it is and add or take away from 0, 180 or 360 as required.

Question 6

What are the angles for the cast diagram?

Answer 6

East is 0, North is 90, West is 180 and South is 270.

Question 7

How do you work out x for values of z sin, z cos or z tan x = y?

Answer 7

Divide 90 by z and use this value to work out the north east and south and west values where East = 0, North = z, West = 2z etc. Use the Cast diagram like you would otherwise.

Question 8

How do you work out x for values of sin, cos or tan x-z = y?

Answer 8

Find the value of x-z using the calculator and use a cast diagram to wok out the other, then rearrange for x.