Table of Contents
Cos 30 Degree Introduction
A cosine function is a trigonometric function that relates the angle of a point on a unit circle to the corresponding point on the hypotenuse. The cosine function is abbreviated as “cos” and is denoted by the symbol “cos”. The cosine function is periodic, meaning that its value repeats after a certain interval. The period of the cosine function is 2π, which means that the value of the cosine function repeats every 2π radians.
The Alternative form of Cos 30
The alternative form of Cos 30 degrees is 1/2.
Proof for Cos 30 Degrees
- We can use the cosine law to find the cosine of 30 degrees.
- The cosine of 30 degrees is equal to the cosine of the opposite side divided by the cosine of the adjacent side.
- The opposite side is 10 units long.
- The adjacent side is 20 units long.
- The cosine of 10 divided by the cosine of 20 is equal to 0.5.
Using the Trigonometric Approach
The trigonometric approach to this problem uses the inverse sine function, arcsin.
arcsin(x) = inverse sine of x
Since the inverse sine of 0 is undefined, this function will not be able to solve the problem for x when x = 0.
When x is not equal to 0, the arcsin function will return the angle in radians that is the inverse of the sine of x.
In order to find the length of the hypotenuse, the length of the opposite side and the length of the adjacent side need to be calculated.
The opposite side is the side opposite the angle, and is found by using the formula:
opposite side = sin(angle)
The adjacent side is the side adjacent to the angle, and is found by using the formula:
adjacent side = cos(angle)
The length of the hypotenuse is found by using the Pythagorean theorem, which states that the length of the hypotenuse is the square root of the sum of the squares of the other two sides.
This can be written mathematically as:
hypotenuse = √(opposite side^2 + adjacent side^2)
Plugging in the values for the opposite side and adjacent side gives:
hypotenuse = √(sin(angle)^2 + cos(angle)
