Cos Calculator

Calculate the cosine (cos) of any angle in degrees instantly with our free online Cos Calculator. Ideal for GCSE and A-Level students, engineers, surveyors, architects, programmers and anyone working with trigonometry.

✔ Degrees & radians • ✔ Accurate cosine values • ✔ Instant calculation • ✔ Free calculator

What is a Cos Calculator?

A Cos Calculator calculates the cosine (cos) of any angle in seconds. Cosine is one of the three fundamental trigonometric functions, together with sine (sin) and tangent (tan). It is used throughout mathematics, engineering, architecture, navigation, robotics and computer graphics.

Simply enter an angle in degrees and the calculator instantly converts it into radians, calculates the cosine value, determines the quadrant and displays the point on the unit circle.

What is Cosine?

In a right-angled triangle, cosine is the ratio of the adjacent side to the hypotenuse.

For example, if the adjacent side measures 5 units and the hypotenuse measures 10 units:

• cos(θ) = 5 ÷ 10
• cos(θ) = 0.5

This means the cosine of the angle is 0.5.

Understanding the Unit Circle

Cosine can also be defined using the unit circle. Every angle corresponds to a point on the circle.

• X-coordinate = cos(θ)
• Y-coordinate = sin(θ)

Your calculator visualises this point and identifies which quadrant the angle belongs to.

Common Cosine Values

Angle	Radians	Cosine
0°	0	1.000000
30°	π/6	0.866025
45°	π/4	0.707107
60°	π/3	0.500000
90°	π/2	0.000000
180°	π	-1.000000

Worked Examples

Example 1 — cos(60°)

• Angle = 60°
• Radians = 1.047198
• Quadrant = I
• Result = 0.500000

Example 2 — cos(45°)

• Angle = 45°
• Radians = 0.785398
• Quadrant = I
• Result = 0.707107

Example 3 — cos(180°)

• Angle = 180°
• Radians = 3.141593
• Quadrant = III
• Result = -1.000000

Where is Cosine Used?

Cosine in Physics

Cosine is frequently used when resolving vectors into horizontal and vertical components.

For example, the horizontal component of a force is calculated as:

This formula is used extensively in mechanics, engineering and structural analysis.

Sine, Cosine and Tangent

Function	Definition
sin	Opposite ÷ Hypotenuse
cos	Adjacent ÷ Hypotenuse
tan	Opposite ÷ Adjacent

Things to Remember

• Cosine values always range from -1 to 1.
• Cosine is positive in Quadrants I and IV.
• Cosine is negative in Quadrants II and III.
• The calculator supports negative angles.
• Angles greater than 360° are automatically handled.

Frequently Asked Questions

What is cos(0°)?

cos(0°) = 1

What is cos(60°)?

cos(60°) = 0.5

What is cos(90°)?

cos(90°) = 0

Can cosine be negative?

Yes. Cosine is negative in Quadrants II and III, so many angles between 90° and 270° produce negative values.

Does this calculator use degrees?

Yes. Simply enter the angle in degrees and the calculator converts it automatically.

✔ Free • ✔ Fast • ✔ No signup required • ✔ No DATA collected

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