Cos 0 Degrees

Cos 0 is equal to 1. Cosine Ratio in Trigonometry is defined as the ratio of the base to the hypotenuse. In Trigonometry, the angle θ is between the base and the hypotenuse of the right-angled triangle. Cosine Ratio is one of six ratios used in trigonometry. Trigonometric Ratios are the ratio of two sides of a triangle calculated for a given angle. Trigonometry is made up of two words trigono and metron where trigono means in triangle and metron means to measure the angles.

In this article, we will discuss Cos 0. How the value of cos 0 is derived? With the help of trigonometry, we can do accurate measurements of any object such as buildings, monuments, etc.

What is Cos 0?

Cos 0 is the ratio of base and hypotenuse when the angle between them is 0°. The value of Cos 0 degree is 1. Cos is one of six trigonometry ratios in a right triangle. Cos is a short form of cosine function. The values of the trigonometry ratio are defined in terms of angles such as 0°, 30°, 60°, and 90 degrees in a triangle. The value of cos 0 is 1 and can be calculated by various methods such as using a right triangle and unit circle. When one of the angles becomes 0 then cos 0 is calculated in a right triangle.

Cos 0 = 1

How to Find the Value of Cos 0 Degree?

The value of cos 0 is 1. There are two methods for finding the value of cos 0. These two methods are mentioned below:

• Cos 0 using Trigonometry
• Cos 0 using Unit Circle

Both the method for finding the value of cos 0 is discussed below :

Cos 0 using Trigonometry

Cosine is represented as the ratio of base and hypotenuse. In the similar other trigonometric ratios are also expressed as the ratio of sides of a right angled triangle. Hence, all the trigonometric ratios can be expressed in the form of other i.e. cos can be expressed in terms of sin, tan etc. Hence, knowing other trigonometric functions can also help in finding value of cos 0 degrees. Let’s learn the equivalent expression of cos 0

• cos 0 = ±√1 – sin²0
• cos 0 = cos (- 0)
• cos 0° = sin (90°-0°)
• cos 0° = sin (90° + 0° )
• cos 0° = -cos (180°- θ)
• cos 0° = 1/sec 0°
• cos 0° = cos (0° + n × 360° )
• cos 0 = cos (2nπ + 0)

Read More about Trigonometry.

Cos 0 Using Unit Circle

In Cos 0 using Unit Circle by drawing a circle of radius r unit circle, we will find the value of cos 0 degree. It will form 0 degree with the x- coordinate of circle. The point where x-coordinate intersect the circle is value of cos 0 degree. It will intersect at (0, 1) so the value of cos 0 degree is 1. From the given figure below when base and hypotenuse overlap then value of cos 0 is equal to 1, because length of both base and hypotenuse will become unit 1 as, it intersect at the boundary of circle.

Cos 0 using unit circle

What are Trigonometric Ratios?

Trigonometric Ratios are the ratio of sides of a right angled triangle for the specific angle. The sides adjacent to the assumed angle θ are hypotenuse and the base. Hypotenuse is the longest side of the right triangle while the other side is the base. There are six trigonometric ratios namely sin, cos, tan, cot, sec and cosec. The expression of these ratio in terms of sides of right triangle for a given angle θ is mentioned below:

• Sin θ = Perpendicular/Hypotenuse
• Cos θ = Base/Hypotenuse
• Tan θ = Perpendicular/Base
• Cot θ = Base/Perpendicular
• Sec θ = Hypotenuse/Base
• Cosec θ = Hypotenuse/Perpendicular

Trigonometry Ratio Table

Trigonometry Ratio Table contain the value of trigonometry ratios at standard angles such as 0°, 30°, 45°, 60° and 90°. The trigonometry ratio table is attached below:

Solved Examples on Cos 0 Degrees

Example 1: Find the value of given expression: cos 0 + cos 90 + cos 60

Solution:

Cos 0 = 1 , cos 90 = 0 , cos 60 = 1/2

Hence, cos 0 + cos 90 + cos 60 = 1 + 0 + 1/2 = 3/2 = 1.5

Example 2: Evaluate the given expression: Sin 90 + cos 0

Solution:

sin 90 = 1, cos 90 = 0

Hence, sin 90 + cos 0 = 1 + 0 = 1

Example 3: Find the value of given expression: √2(Sin 45 + cos 45) + cos 0 + cos 90 + sin 0 + sin 90

Solution:

sin 45 = 1/√2, cos 45 = 1/√2, cos 0 = 1, cos 90 = 0, sin 0 = 0, sin 90 = 1

√2(Sin 45 + cos 45) + cos 0 + cos 90 + sin 0 + sin 90

Putting the values we get

√2(1/√2 + 1/√2) + 1 + 0 + 0 + 1

= √2(2/√2) + 2

= 2 + 2 = 4

Example 4: Evaluate the given expression: Sin 30 + cos 0 + tan 45 + cot 45 .

Solution:

sin 30 = 1/2 , cos 0 = 1, tan 45 = 1, cot 45 =1

Putting the values in the expression we get

= 1/2 + 1 + 1 + 1

= 7/2

Example 5: Find the value of given expression: Cos²0 + sin²0 .

Solution:

cos 0 = 1 , sin 0 = 0

= (1)² + (0)²

= 1 (by trigonometry identity also : sin²θ + cos²θ = 1)

Practice Questions on Cos 0 Degree

Q1: Evaluate the expression: cos 0 + cos 90 + cos 45

Q2: Find the value of given expression: sin 90 × sin 45 × sin 30 × cos 0 × cos 90

Q3: Evaluate the following expression: tan 0 + tan 30 + tan 60

Q4: Find the value of: sec 90 + sec 0

FAQs on Cos 0 Degrees

1. What is the Value of cos 0°?

The value of cos 0° is 1.

2. How the Value of cos of any Angle is calculated?

The value of cos of any angle using unit circle concept for the given angle.

3. What is the Formula of Cos θ?

The cos of angle is calculated by dividing length of base by length of hypotenuse.

cos θ = base/hypotenuse

4. When is Cos 0?

cos 0 is calculated when in unit circle of radius r, the x-coordinate lies on point (0,1).

5. Cos 0 is Equal to?

Cos 0 is equal to 1.

6. Is Cos 0° equal to Sin 90°?

Yes, value of both cos 0° and sin 90° is equal to 1.

7. Why is Cos 0° Equal to 1?

Value of cos 0 is equal to 1 because when hypotenuse overlaps on base of triangle inside unit circle, then its coordinate lies at point (1,0). The value of x- coordinate is 1.