students corner(form 3/4)
.Solve for X in the range 0 ≤ X ≤ 360
4 Cos(2x- 30 ) = -0.96
solution:
>divide through by amplitude which in this case is 4 to obtain
Cos(2x- 30 ) = -0.24
>find cos-1 to get
(2x-30 )= -103.89 and 103.89....
{ you must always get 2 answers
for cosine the inverse cosine gives the same number but positive as first answer and the second value is negative...
this stems from the fact that
cos(y)=Cos(-y)
ie cos(3=cos (-3 which is 0.8660
so cos-1 (0.866 = -30 , 30
}
thus
(2x-3=cos-1(-0.24)
(2x-3= -103.89 , 103.89
Remember cosine is PERIODIC,ie it repeats itself after some degrees and default is 360 degrees thus cos(3=cos(-3=cos(30+36 =cos(-30+36=cos(390+36
thus -30,30,330,390,690,750,..keep adding 360 and the cosine values are the same....
applying this then
(2x-3 =-103.89,103.89,256.11,463.89, 616.11 ...keep adding 360 to get other values
2x = -73.89 ,133.89,286.11 , 493.89 ,646.11 ....adding 30 from Left hand side and dropping the bracket
x = -36.95,66.95, 143.05 , 246.95 , 323.05 ....dividing through by 2 to get x values.....
x= 66.95, 143.05 , 246.95 , 323.05 ....ignoring value that are not in the range 0 ≤ X ≤ 360
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Try:
Solve for X in the range 0 ≤ X ≤ 360
-5 Cos(3x- 8 = -2
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