Cos 30 Degrees Proof
There are two approaches to deriving the value of cos 30 degrees, they are:
- Theoretical approach
- Practical approach
Theoretical Approach
In the theoretical approach, the value of cos 30 degrees is obtained by observing the sides of the right-angled triangle and using Pythagoras theorem. It can be seen that if the angle of the right angle triangle is 30, we can find out the length of the opposite side, which will be half the length of the hypotenuse, but in order to find the value of cos 30, we require the length of the adjacent side as well (base of the triangle).
Applying Pythagoras theorem:
OA2 = OB2 + AB2
⇒ d2 = OB2 + (d/2)2
⇒ d2 = OB2 + d2/4
⇒ OB2 = d2 – d2/4
⇒ OB2 = 3d2/4
⇒ OB = √3d/2
The value of cosine can be found by finding the ratio of the base to its hypotenuse; therefore, in this case, cos 30 degrees will be:
Cos 30° = OB/OA
⇒ Cos 30° = √3d/2 × 1/d
⇒ Cos 30° = √3/2
Practical Approach
The value of cos 30 degrees can also be observed using the practical approach. In the practical approach, the right-angled triangle is drawn, making an angle of 30 degrees, and then the value of cos 30° is observed. Following are the steps to draw the triangle:
- Take a point O and draw and line.
- Using the line as the baseline, make a 30-degree angle from the protector.
- Draw a line from that angle found. Take any random length and draw an arc to decide where the line shall stop. Name it, Point A.
- Draw the perpendicular (Vertical line) to the base from the intersection formed by the arc and the line. They will meet at B.
Cos 30 Degrees
Cos 30 Degrees: The value of cos 30 degrees in trigonometry is √3/2. In a right-angled triangle, cosine is the ratio of the base and hypotenuse. When the angle of the right-angled triangle is 30°, cos 30° is required. In fraction form, cos 30° is √3/2; in decimal form, the value is 0.8660.
Let’s understand how the value of cos 30° is obtained with examples.
Table of Content
- What is the Value of Cos 30 Degrees?
- How to Find the Value of Cos 30 Degrees
- Cos 30 Degrees – Methods to Find
- Cos 30 Degrees in Terms of Trigonometric Functions
- Cos 30 Degrees Using Unit Circle
- Cos 30 Degrees Proof
- Theoretical Approach
- Practical Approach
- People Also Read:
- Solved Examples on Cos 30 Degrees