4cos(3x) + 4 = 0 Subtract 4 from both sides: 4cos(3x) = -4 Divide by 4: cos(3x) = -1
The cosine function equals -1 when the angle is 180 degrees, but since 3x is the angle, we need to find all solutions between 0 and 360 degrees. This can be done by dividing 180 by 3, which gives us 60 degrees.
So the solutions for cos(3x) = -1 are: 3x = 180 + 360n, where n is an integer
√3 - tan(2x) = 0 tan(2x) = √3 Since tan(60 degrees) = √3, this means that 2x = 60 degrees or 240 degrees. Therefore, the solution for √3 - tan(2x) = 0 is: x = 30 degrees or x = 120 degrees
To solve the equations given:
4cos(3x) + 4 = 0Subtract 4 from both sides:
4cos(3x) = -4
Divide by 4:
cos(3x) = -1
The cosine function equals -1 when the angle is 180 degrees, but since 3x is the angle, we need to find all solutions between 0 and 360 degrees. This can be done by dividing 180 by 3, which gives us 60 degrees.
So the solutions for cos(3x) = -1 are:
√3 - tan(2x) = 03x = 180 + 360n, where n is an integer
tan(2x) = √3
Since tan(60 degrees) = √3, this means that 2x = 60 degrees or 240 degrees.
Therefore, the solution for √3 - tan(2x) = 0 is:
x = 30 degrees or x = 120 degrees