SOLUTION: Determine the general solution to the following equation in degrees, rounded to the nearest hundredth. 4 cos(15(x+30°))+1=−2

Algebra ->  Trigonometry-basics -> SOLUTION: Determine the general solution to the following equation in degrees, rounded to the nearest hundredth. 4 cos(15(x+30°))+1=−2      Log On


   

Question 1193099: Determine the general solution to the following equation in degrees, rounded to the nearest hundredth.
4 cos(15(x+30°))+1=−2
Found 3 solutions by MathLover1, Edwin McCravy, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

4cos%2815%28x%2B30%29%29%2B1=-2
4cos%28%28x%2B30%29%29=-2-1
cos%2815%28x%2B30%29%29=-3%2F4
15%28x%2B30%29=cos%5E-1%28-3%2F4%29
15%28x%2B30%29=2.4188584-> radians, convert to degrees:2.4188584=138.59°
15x%2B450=138.59°
15x=138.59-450°
15x=-311.41°
x=-311.41%2F15°
x=-20.76°


Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!

The other tutor gave only one solution, not the general solution.

4cos%2815%28x%2B30%5Eo%29%5E%22%22%29%2B1%22%22=%22%22-2

4cos%2815%28x%2B30%5Eo%29%5E%22%22%29%22%22=%22%22-3

cos%2815%28x%2B30%5Eo%29%5E%22%22%29%22%22=%22%22-3%2F4

cos%2815x%2B450%5Eo%29%5E%22%22%29%22%22=%22%22-3%2F4

Any integer multiple of 360o positive, negative
or 0 may be added to any angle without changing the value
of any of its 6 trig ratios.  So we add -360o:

cos%2815x%2B450%5Eo-360%5Eo%29%5E%22%22%29%22%22=%22%22-3%2F4

cos%2815x%2B90%5Eo%29%5E%22%22%29%22%22=%22%22-3%2F4

cos%2815x%5E%22%22%29cos%2890%5Eo%29-sin%2815x%5E%22%22%29sin%2890%5Eo%29%22%22=%22%22-3%2F4

cos%2815x%5E%22%22%29%280%29-sin%2815x%5E%22%22%29%281%29%22%22=%22%22-3%2F4

-sin%2815x%5E%22%22%29%22%22=%22%22-3%2F4

sin%2815x%5E%22%22%29%22%22=%22%223%2F4

15x%22%22=%22%22matrix%281%2C3%2C48.59%5Eo%2B360%5Eo%2An%2Cor%2C131.41%5Eo%2B360%5E0%2An%29

x%22%22=%22%22matrix%281%2C3%2C3.24%5Eo%2B24%5Eo%2An%2Cor%2C8.76%5Eo%2B24%5Eo%2An%29,
when n is any integer.

Edwin

Answer by ikleyn(52915) About Me  (Show Source):
You can put this solution on YOUR website!
.

For future generations of students who will read this post:

        - use the solution by  Edwin, which is correct.

        - do not use / ignore the solution by @MathLover1,  which is incorrect,  since it is incomplete.