root 3 cos (4 pi/3 = root 3/2
The equation you have given is incorrect. There is a typo in the equation.
Corrected equation:
√3 cos(4π/3) = -√3/2
When we evaluate cos(4π/3), we can use the unit circle to find the corresponding angle. At 4π/3 radians, the angle is located in the third quadrant.
In the third quadrant, the x-coordinate (cosine value) is negative. So, cos(4π/3) = -1/2.
Substituting this value back into the equation:
√3 cos(4π/3) = √3 * (-1/2) = -√3/2
Therefore, the correct equation is -√3/2.
To confirm if the equation root 3 cos (4 pi/3) is equal to root 3/2, we can evaluate the cosine of 4 pi/3.
The angle 4 pi/3 is equivalent to 240 degrees in degrees.
We can use the unit circle to evaluate the cosine of 240 degrees or 4 pi/3.
On the unit circle, starting from the positive x-axis, you move counterclockwise to the angle of 240 degrees.
At this angle, the x-coordinate (cosine value) is -1/2, and the y-coordinate (sine value) is -√3/2.
So, root 3 cos (4 pi/3) is equal to root 3 * (-1/2), which simplifies to -root 3/2.
Therefore, root 3 cos (4 pi/3) is not equal to root 3/2.