4.1 Sine and Cosine Graphing
Sine
Use your knowledge of the unit circle to fill in the table with exact values.
x
0
/4
π
π/2
3π
/4
π
/4
3π
/2
7π
/4
2π
5π
y = sin x
0
1
/√2 ≈ .7
1
1
/√2 ≈ .7
0
-1/√2 ≈ -.7
-1
-1/√2 ≈ -.7
0
*choose values that go all the way around the circle!
Example 1-- Use your graph to find all the values of x between 0 ≤ x ≤ 2π for which
sin x = -1.
Example 2-- What is the domain of y = sin x ?
Example 3-- What is the range of y = sin x ?
Cosine
Use your knowledge of the unit circle to fill in the table with exact values.
x
0
π/4
π/2
3π
/4
π
5π
/4
3π
/2
7π
/4
2π
y = cos x
*choose values that go all the way around the circle!
1
/√2
0
-1/√2
1
-1
-1/√2
0
1/√2
1
Example 4-- What do you notice about the sine and cosine curves?
Example 5-- What is the domain of y = cos x ?
Example 6-- What is the range of y = cos x ?
Example 7-- Use your graph to find all the values of x between 0 ≤ x ≤ 2π for which
cos x = 0.
Remember how to determine if a function is
even or odd from chapter 1 in Precalculus?
even: f(x) = f(-x)
*symmetric about the y-axis
odd: f(-x) = -f(x)
*symmetric about the origin
Example 8-- Determine if the sine function
is even, odd, or neither.
Example 9-- Determine if the cosine function is even, odd, or neither.
Example 10-- Use the fact that cosine is even to find the following...
cos (-300)
Example 11-- Use the fact that sine is odd to find the following...
sin (-300)
page 183
7, 10, 13­16, 25­34
4.1 Tangent, Cotangent, Secant, and Cosecant graphing
Tangent
Use your knowledge of the unit circle to fill in the table with exact values.
x
0
π/6
π/4
π/3
y = tan x =
Cotangent
x
y = cot x =
0
π/6
π/4
π/3
π/2
2π/3
3π
/4
5π
/6
π
sin x
cos x
cos x
sin x
Cosecant
y = csc x
x
0
π/4
π/2
3π
/4
y=sin x 1/sin x
π
/4
3π
/2
7π
/4
2π
5π
Secant
y = sec x
x
0
π/4
π/2
3π
/4
π
5π
/4
3π
/2
7π
/4
2π
y=cos x 1/cos x
page 183
8, 9, 11, 12
17-24