The value of cos^-1(-(sqrt3)/2) is what?
The question asks you to find the inverse cosine (arccosine) of -sqrt(3)/2
Think about your memory values and special triangles. Where is cosine(theta) equal to -sqrt(3)/2?
To find the value of cos^-1(-(sqrt3)/2), we need to understand what the inverse cosine function represents.
The inverse cosine function, denoted as cos^-1 or arccos, gives us the angle whose cosine equals a given value. In other words, it helps us find the angle θ for which cos(θ) is equal to a particular value.
In this case, we are looking for the value of cos^-1(-(sqrt3)/2). To find this angle, we can refer to the unit circle and the values of cosine for different angles.
The unit circle is a circle with a radius of 1, centered at the origin of a coordinate plane. The cosine of an angle can be determined by looking at the x-coordinate of the corresponding point on the unit circle.
The given value, -(sqrt3)/2, represents the cosine of an angle. We need to find the angle θ for which cos(θ) equals -(sqrt3)/2.
Looking at the unit circle, we can observe that the angle θ is 5π/3 or 300 degrees. This is because at 5π/3 or 300 degrees, the x-coordinate of the corresponding point on the unit circle is -(sqrt3)/2.
Therefore, the value of cos^-1(-(sqrt3)/2) is 5π/3 or 300 degrees.