Angle Cosine Inverse:

To find the value of cos^-1(3/4), we need to understand the concept of the inverse cosine function. The inverse cosine, or cos^-1, is also known as arccosine. It is the inverse function of the cosine (cos) function.

Understanding Cosine Function:

The cosine function is a mathematical function that relates the angle of a right triangle to the ratio of the adjacent side to the hypotenuse. In other words, it gives the ratio of the length of the adjacent side to the length of the hypotenuse. The cosine function is defined for angles ranging from 0 to 180 degrees, or 0 to π radians.

Finding the Value of cos^-1(3/4):

To find the value of cos^-1(3/4), we need to determine the angle whose cosine is equal to 3/4. In other words, we need to find the angle θ such that cos(θ) = 3/4.

To solve this, we can use the inverse cosine function. The inverse cosine function takes a ratio as input and gives the corresponding angle as output. In this case, we want to find the angle whose cosine is 3/4.

Solution:

Using the inverse cosine function, we can write:

θ = cos^-1(3/4)

To evaluate this expression, we can use a calculator or reference table that provides the values of inverse trigonometric functions.

When we evaluate cos^-1(3/4), we find that it is equal to approximately 41.41 degrees or 0.72 radians.

Therefore, the value of cos^-1(3/4) is approximately 41.41 degrees or 0.72 radians.

Summary:

- The inverse cosine function, or cos^-1, is the inverse of the cosine function.
- It takes a ratio as input and gives the corresponding angle as output.
- To find the value of cos^-1(3/4), we need to determine the angle whose cosine is equal to 3/4.
- Using the inverse cosine function, we find that cos^-1(3/4) is approximately 41.41 degrees or 0.72 radians.