Example
What do you think the graph of \(y = \cos 2x^\circ\) would look like?
- amplitude = 1, so the distance between the maximum and minimum values is 2
- number of waves = 2 (period is 360˚ ÷ 2 = 180˚)
- graph has not moved up or down
- maximum turning point when \(y = 1\) and minimum turning point when \(y = - 1\)
The graph looks like:
Now try the example questions below.
Question
What do you think the graph of \(y = 3\cos x^\circ\) would look like?
- amplitude = 3, so the length between the maximum and minimum values is 6
- number of waves = 1 (period is 360˚ ÷ 1 = 360˚)
- graph has not moved up or down
- maximum turning point when \(y = 3\) and minimum turning point when \(y = - 3\)
This graph looks like:
Question
What do you think the graph of \(y = \cos x^\circ - 4\) would look like?
- amplitude = 1, so the length between the maximum and minimum values is 2
- number of waves = 1 (period is 360˚ ÷ 1 = 360˚)
- graph has not moved down by 4 (since c < 0)
- maximum turning point when \(y = 1 -4 = -3\) and minimum turning point when \(y = - 1 - 4 = -5\)
This graph looks like:
Question
What does the graph of \(y = 5\cos 2x^\circ\) look like?
- amplitude = 5, so the length between the maximum and minimum values is 10
- number of waves = 2 (period is 360˚ ÷ 2 = 180˚)
- graph has not moved up or down
- maximum turning point when \(y = 5\) and minimum turning point when \(y = -5\)
This graph looks like: