Statements | Reasons |
Definition of cosine = adjacent / hypotenuse | |
a = y cos(x- 90)° | Multiplication Property of Equality |
a = y (cos(-(90-x))) | Distributive Property (Factored out -1) |
a = y (cos(90 - x)) | cos(-A) = cos(A) |
a = y sin(x) | cos (90 - A) = sin(A) |
Statements | Reasons |
Definition of sine = opposite / hypotenuse | |
Substitution (Sub a = y sin(x) into previous step) | |
Square both sides | |
2 - 2cos(x) = 3 (1 - cos2x) | Multiplication Property of Equality |
2 - 2cos(x) = 3 - 3 cos2x | Distributive Property |
3 cos2x - 2 cos(x) - 1 = 0 | Addition Property of Equality |
(3 cos(x) + 1) (cos(x) - 1) = 0 | Factor (Distributive Property) |
cos (x) = -1/3 or cos(x) = 1 | Set each factor = 0 (Mult. Prop. of 0) Muliplication Property of Equality |
so x = 109.4712206° | Inverse Cosine |