The document discusses sine and cosine curves. It defines key terms like amplitude and period for sine and cosine functions, and how transformations affect these values. Examples are provided to find the amplitude, period, and equation for various sine and cosine graphs. Methods to solve equations involving sine and cosine functions either algebraically or graphically are also described.
3. Amplitude
The amplitude of y = sin x and
y = cos x is 1.
y = 2 sin x has amplitude:
y = - ½ cos x has amplitude:
So, for y = A sin x and y = A cos x
(A≠0):
amplitude = |A|
2
½
10. You Try!
Give the amplitude, period, and an
equation of the graph shown.
11. Solving Equations
To solve algebraically:
Isolate the “trig part”
Use inverse trig to find an angle
Find others within the restrictions
Solve for x
12. Example:
Solve 6 sin 2x = 5 for 0 ≤ x < 2π to
the nearest hundredth of a radian.
13. Solving Graphically
Graph y = each side of the equation.
Find x-coordinates of all intersection
points within the restrictions.