Writing Equations for Trigonometric Functions
Author: Laura Kinnel

For each problem, write an equation for the given graph in terms of sine and then in terms of cosine. In the input line, type "f(x) =" followed by your equation, and press Enter to see if your equation matches the graph. (Be sure the "Show my graph" box is checked.)

(For some problems, it may be helpful to use the pink and blue sliders. The pink slider moves a vertical line up and down the plane in increments of 1/2, while the blue slider moves a vertical line across the plane in increments of π/12 .)

Type "f(x) =" followed by your equation and then press Enter to see if your equation matches the given graph. (Make sure the "Show my graph" box is checked.)

Show y = sin x

Show y = cos x

π

2π

-π

-2π

π/2

3π/2

-π/2

-3π/2

5π/2

-5π/2

3π

-3π

Show my graph

s(x) = sin(x)
c(x) = cos(x)
a = false
b = false
f01(x) = sin(x)
f02(x) = sin(x + 3.141592653589793 / 4)
f03(x) = sin(x + 3 * 3.141592653589793 / 4)
A = (3.141592653589793, 0)
f04(x) = sin(x - 2 * 3.141592653589793 / 3)
Problem = 1 (slider from 1 to 40, step 1)
B = (6.283185307179586, 0)
f05(x) = sin(x - 7 * 3.141592653589793 / 6)
f06(x) = sin(x + 5 * 3.141592653589793 / 12)
C = (-3.141592653589793, 0)
D = (-6.283185307179586, 0)
f07(x) = 3 * sin(x)
f08(x) = 0.5 * cos(x)
f09(x) = -2 * sin(x)
f10(x) = -4 * sin(x)
f11(x) = 1.5 * cos(x + 3.141592653589793 / 4)
f12(x) = 3 * cos(x + 3.141592653589793 / 6)
f13(x) = 2 + cos(x)
f14(x) = -1 + sin(x)
E = (1.5707963267948966, 0)
F = (4.71238898038469, 0)
f15(x) = 3 + 2 * sin(x)
f16(x) = 1 - 4 * cos(x)
G = (-1.5707963267948966, 0)
H = (-4.71238898038469, 0)
f17(x) = -3 + 2 * cos(x - 3.141592653589793 / 4)
f18(x) = 2 - 3 * sin(x + 3.141592653589793 / 3)
f19(x) = cos(2 * x)
f20(x) = cos(3 * x)
f21(x) = sin(2 * x)
f22(x) = sin(6 * x)
f23(x) = sin(x / 2)
f24(x) = 3 + cos(2 * x)
f25(x) = -1 + sin(4 * x)
f26(x) = -2 + 3 * cos(3 * x)
f27(x) = 2.5 + 1.5 * cos(x / 3)
f28(x) = 1 - 2 * sin(3 * x)
f29(x) = 3 + sin(2 * (x + 3.141592653589793 / 3))
v = -9.42477796076938 (slider from -10.210176124166829 to 10.21, step 0.2617993877991494)
d: x = v
h = -4.5 (slider from -6 to 5, step 0.5)
e: y = h
f30(x) = -4 + cos(3 * (x - 3.141592653589793 / 2))
f31(x) = 2 - sin(0.5 * (x - 3.141592653589793 / 4))
I = (7.853981633974483, 0)
J = (-7.853981633974483, 0)
K = (9.42478, 0)
L = (-9.42477796076938, 0)
f32(x) = 1 + 3 * sin((x + 3.141592653589793) / 3)
f33(x) = -2 + 0.5 * cos(3 * (x - 3.141592653589793 / 2))
f(x) = 0
g = true
text1: "f(x) = " + f
M = (-13.409929078014187, 7.039716312056737)
N = (9.5, 7.04)
O = (9.5, 5.24)
P = (-13.409929078014187, 5.239716312056737)
poly1, m, n, o, p = Polygon(M, N, O, P)
t = 100
f34(x) = 0.5 + 2.5 * cos(2 * (x + 3.141592653589793 / 6))
f35(x) = sin(3.141592653589793 * x)
F35_1 = (0, 0)
F35_2 = (1, 0)
F35_3 = (2, 0)
f36(x) = -cos(0.5 * 3.141592653589793 * x)
F36_1 = (0, -1)
F36_2 = (2, 1)
F36_3 = (4, -1)
F36_4 = (1, 0)
F36_5 = (3, 0)
F36_6 = (5, 0)
F35_4 = (0.5, 1)
F35_5 = (1.5, -1)
F35_6 = (2.5, 1)
f37(x) = 3 + 2 * sin(0.25 * 3.141592653589793 * x)
F37_1 = (0, 3)
F37_2 = (4, 3)
F37_3 = (8, 3)
F37_4 = (-6, 5)
F37_5 = (-2, 1)
F37_6 = (2, 5)
f38(x) = -1 - 3 * sin(3.141592653589793 / 3 * x)
F38_1 = (0, -1)
F38_2 = (3, -1)
F38_3 = (6, -1)
F38_4 = (1.5, -4)
F38_5 = (4.5, 2)
F38_6 = (7.5, -4)
f39(x) = 2 + 0.5 * sin(0.4 * 3.141592653589793 * (x - 1))
F39_1 = (1, 2)
F39_2 = (3.5, 2)
F39_3 = (6, 2)
F39_4 = (-0.25, 1.5)
F39_5 = (-2.75, 2.5)
F39_6 = (-5.25, 1.5)
f40(x) = 1 + 3 * sin(2 * 3.141592653589793 / 3 * (x - 2))
F40_1 = (1.25, -2)
F40_2 = (2.75, 4)
F40_3 = (4.25, -2)