Answer to Question #163882 in Trigonometry for SAMUEL KASSAPA

Question

y=5+8cos[pi(x-1)]

y=2+3cos2x

draw 2 periods

or 2 cycles

Answer 1

y = 5 + 8 Cos(pi(x-1))

Lets take x = 0 to 4 in steps of 0.2

x =0,   Cos(PI*(x-1)) = Cos(PI*(0-1)) =-1, Therefore, y(1) =-3
x =0.2, Cos(PI*(x-1)) = Cos(PI*(0.2-1)) =-0.80902, Therefore, y(2) =-1.4721
x =0.4, Cos(PI*(x-1)) = Cos(PI*(0.4-1)) =-0.30902, Therefore, y(3) =2.5279
x =0.6, Cos(PI*(x-1)) = Cos(PI*(0.6-1)) =0.30902, Therefore, y(4) =7.4721
x =0.8, Cos(PI*(x-1)) = Cos(PI*(0.8-1)) =0.80902, Therefore, y(5) =11.4721
x =1, Cos(PI*(x-1)) = Cos(PI*(1-1)) =1, Therefore, y(6) =13
x =1.2, Cos(PI*(x-1)) = Cos(PI*(1.2-1)) =0.80902, Therefore, y(7) =11.4721
x =1.4, Cos(PI*(x-1)) = Cos(PI*(1.4-1)) =0.30902, Therefore, y(8) =7.4721
x =1.6, Cos(PI*(x-1)) = Cos(PI*(1.6-1)) =-0.30902, Therefore, y(9) =2.5279
x =1.8, Cos(PI*(x-1)) = Cos(PI*(1.8-1)) =-0.80902, Therefore, y(10) =-1.4721
x =2, Cos(PI*(x-1)) = Cos(PI*(2-1)) =-1, Therefore, y(11) =-3
x =2.2, Cos(PI*(x-1)) = Cos(PI*(2.2-1)) =-0.80902, Therefore, y(12) =-1.4721
x =2.4, Cos(PI*(x-1)) = Cos(PI*(2.4-1)) =-0.30902, Therefore, y(13) =2.5279
x =2.6, Cos(PI*(x-1)) = Cos(PI*(2.6-1)) =0.30902, Therefore, y(14) =7.4721
x =2.8, Cos(PI*(x-1)) = Cos(PI*(2.8-1)) =0.80902, Therefore, y(15) =11.4721
x =3, Cos(PI*(x-1)) = Cos(PI*(3-1)) =1, Therefore, y(16) =13
x =3.2, Cos(PI*(x-1)) = Cos(PI*(3.2-1)) =0.80902, Therefore, y(17) =11.4721
x =3.4, Cos(PI*(x-1)) = Cos(PI*(3.4-1)) =0.30902, Therefore, y(18) =7.4721
x =3.6, Cos(PI*(x-1)) = Cos(PI*(3.6-1)) =-0.30902, Therefore, y(19) =2.5279
x =3.8, Cos(PI*(x-1)) = Cos(PI*(3.8-1)) =-0.80902, Therefore, y(20) =-1.4721
x =4, Cos(PI*(x-1)) = Cos(PI*(4-1)) =-1, Therefore, y(21) =-3

y=2+3cos2x

Lets take x from 0 to 7 at interval of 0.2 as given below

x =0, Cos(2x) = Cos(2*0) =1, Therefore, y(1) =5
x =0.2, Cos(2x) = Cos(2*0.2) =0.92106, Therefore, y(2) =4.7632
x =0.4, Cos(2x) = Cos(2*0.4) =0.69671, Therefore, y(3) =4.0901
x =0.6, Cos(2x) = Cos(2*0.6) =0.36236, Therefore, y(4) =3.0871
x =0.8, Cos(2x) = Cos(2*0.8) =-0.0292, Therefore, y(5) =1.9124
x =1, Cos(2x) = Cos(2*1) =-0.41615, Therefore, y(6) =0.75156
x =1.2, Cos(2x) = Cos(2*1.2) =-0.73739, Therefore, y(7) =-0.21218
x =1.4, Cos(2x) = Cos(2*1.4) =-0.94222, Therefore, y(8) =-0.82667
x =1.6, Cos(2x) = Cos(2*1.6) =-0.99829, Therefore, y(9) =-0.99488
x =1.8, Cos(2x) = Cos(2*1.8) =-0.89676, Therefore, y(10) =-0.69028
x =2, Cos(2x) = Cos(2*2) =-0.65364, Therefore, y(11) =0.039069
x =2.2, Cos(2x) = Cos(2*2.2) =-0.30733, Therefore, y(12) =1.078
x =2.4, Cos(2x) = Cos(2*2.4) =0.087499, Therefore, y(13) =2.2625
x =2.6, Cos(2x) = Cos(2*2.6) =0.46852, Therefore, y(14) =3.4056
x =2.8, Cos(2x) = Cos(2*2.8) =0.77557, Therefore, y(15) =4.3267
x =3, Cos(2x) = Cos(2*3) =0.96017, Therefore, y(16) =4.8805
x =3.2, Cos(2x) = Cos(2*3.2) =0.99318, Therefore, y(17) =4.9796
x =3.4, Cos(2x) = Cos(2*3.4) =0.8694, Therefore, y(18) =4.6082
x =3.6, Cos(2x) = Cos(2*3.6) =0.60835, Therefore, y(19) =3.8251
x =3.8, Cos(2x) = Cos(2*3.8) =0.25126, Therefore, y(20) =2.7538
x =4, Cos(2x) = Cos(2*4) =-0.1455, Therefore, y(21) =1.5635
x =4.2, Cos(2x) = Cos(2*4.2) =-0.51929, Therefore, y(22) =0.44213
x =4.4, Cos(2x) = Cos(2*4.4) =-0.81109, Therefore, y(23) =-0.43328
x =4.6, Cos(2x) = Cos(2*4.6) =-0.97484, Therefore, y(24) =-0.92453
x =4.8, Cos(2x) = Cos(2*4.8) =-0.98469, Therefore, y(25) =-0.95406
x =5, Cos(2x) = Cos(2*5) =-0.83907, Therefore, y(26) =-0.51721
x =5.2, Cos(2x) = Cos(2*5.2) =-0.56098, Therefore, y(27) =0.31705
x =5.4, Cos(2x) = Cos(2*5.4) =-0.19433, Therefore, y(28) =1.417
x =5.6, Cos(2x) = Cos(2*5.6) =0.203, Therefore, y(29) =2.609
x =5.8, Cos(2x) = Cos(2*5.8) =0.56829, Therefore, y(30) =3.7049
x =6, Cos(2x) = Cos(2*6) =0.84385, Therefore, y(31) =4.5316
x =6.2, Cos(2x) = Cos(2*6.2) =0.98619, Therefore, y(32) =4.9586
x =6.4, Cos(2x) = Cos(2*6.4) =0.97283, Therefore, y(33) =4.9185
x =6.6, Cos(2x) = Cos(2*6.6) =0.80588, Therefore, y(34) =4.4177
x =6.8, Cos(2x) = Cos(2*6.8) =0.5117, Therefore, y(35) =3.5351
x =7, Cos(2x) = Cos(2*7) =0.13674, Therefore, y(36) =2.4102