Question

Find the exact value of cos-1 (sqrt 3/2)

Answer 1

The exact value of cos-1 (sqrt 3/2) is 30 degrees or π/6 radians.

Step-by-step explanation:

The question asks to find the exact value of cos-1 (sqrt 3/2). The notation cos-1 represents the inverse cosine function, also known as arccosine. To find the value, we need to determine the angle whose cosine is equal to sqrt 3/2.

The angle whose cosine is sqrt 3/2 is 30 degrees or π/6 radians. This is because the cosine function is positive in the first and fourth quadrants, and its value is sqrt 3/2 at 30 degrees or π/6 radians.

Therefore, the exact value of cos-1 (sqrt 3/2) is 30 degrees or π/6 radians.

Answer 2

The exact value of cos-1 (sqrt 3/2) is 30 degrees or pi/6 radians.

Step-by-step explanation:

The question is asking for the exact value of cos-1 (sqrt 3/2).

Let's first understand what cos-1 represents. The notation cos-1 (or arccos) is the inverse function of the cosine function. It gives us the angle whose cosine is the given value.

In this case, cos-1 (sqrt 3/2) means we need to find the angle whose cosine is sqrt 3/2.

The exact value of cos-1 (sqrt 3/2) is 30 degrees or pi/6 radians. This can be determined by considering the unit circle, where the cosine function gives the x-coordinate of a point on the circle.

Since sqrt 3/2 corresponds to the x-coordinate of the point (cos 30, sin 30) on the unit circle, the angle is 30 degrees or pi/6 radians.