cos2(120degrees) help me solve this please
Is that supposed to be cos^2(120) of cos(2*120) ?
The cosine of 120 is -cos 60 = -1/2.
That may help.
To solve cos2(120 degrees), we can start by using the formula for the double angle identity:
cos(2θ) = cos²(θ) - sin²(θ)
In this case, θ is equal to 120 degrees. So we can substitute 120 degrees into the formula:
cos(2 * 120 degrees) = cos²(120 degrees) - sin²(120 degrees)
Now, let's calculate cos(120 degrees) and sin(120 degrees).
To find cos(120 degrees), we can use the unit circle or trigonometric ratios. In the unit circle, at 120 degrees, the x-coordinate (cos) is -1/2, so cos(120 degrees) = -1/2.
To find sin(120 degrees), we can again refer to the unit circle. At 120 degrees, the y-coordinate (sin) is √3/2, so sin(120 degrees) = √3/2.
Substituting the values into the equation:
cos(2 * 120 degrees) = cos²(120 degrees) - sin²(120 degrees)
cos(240 degrees) = (-1/2)² - (√3/2)²
cos(240 degrees) = 1/4 - 3/4
cos(240 degrees) = -2/4
cos(240 degrees) = -1/2
Therefore, cos2(120 degrees) = -1/2.