Cosine Calculator – Guide & Formulas
Calculate the cosine of any angle instantly. Enter an angle in degrees or radians to find cos(x) with step-by-step results and a unit circle reference.
The Cosine Calculator computes the cosine of any angle. Enter an angle in degrees or radians and instantly receive cos(x) with step-by-step breakdown, the angle on the unit circle, and a reference table of common cosine values.
Key Takeaway
Use the free Cosine Calculator to calculate the cosine of any angle instantly. enter an angle in degrees or radians to find cos(x) with step-by-step results and a unit circle reference. Get instant results with step-by-step explanations.
How to Use the Cosine Calculator
- Enter an angle value in the input field.
- Select degrees or radians as the angle unit.
- The calculator instantly computes the cosine result.
- Review the cosine value, unit circle position, and step-by-step explanation.
The Formula
Variable Definitions
- cos(θ): The cosine of angle θ: the x-coordinate on the unit circle
- θ: The input angle in degrees or radians
- adjacent: The side adjacent to angle θ in a right triangle
- hypotenuse: The longest side of the right triangle
Example: Cosine of 60°
Find cos(60°).
- Step 1: Consider a right triangle with angle θ = 60°.
- Step 2: In a 30-60-90 triangle, the sides are in ratio 1 : √3 : 2.
- Step 3: The side adjacent to 60° is 1, and the hypotenuse is 2.
- Step 4: cos(60°) = adjacent / hypotenuse = 1 / 2 = 0.5.
Frequently Asked Questions
What is cosine?
Cosine (cos) is a trigonometric function that relates an angle in a right triangle to the ratio of the adjacent side to the hypotenuse. On the unit circle, cos(θ) gives the x-coordinate of a point at angle θ.
What is the domain and range of cosine?
The domain of cos(θ) is all real numbers. The range is [-1, 1], meaning cos(θ) always produces values between -1 and 1 inclusive.
What is cos(0°)?
cos(0°) = 1. At 0°, the point on the unit circle is (1, 0), so the x-coordinate (cosine) is 1.
What is cos(90°)?
cos(90°) = 0. At 90°, the point on the unit circle is (0, 1), so the x-coordinate (cosine) is 0.
What is cos(60°)?
cos(60°) = 0.5. This is a fundamental value from the 30-60-90 right triangle where the adjacent side is half the hypotenuse.
How is cosine related to sine?
Cosine and sine are related by the Pythagorean identity: cos²(θ) + sin²(θ) = 1. They are also cofunctions: cos(θ) = sin(90° - θ).
What is the cosine of a negative angle?
Cosine is an even function: cos(-θ) = cos(θ). This means the cosine of a negative angle equals the cosine of the corresponding positive angle.
How do I calculate cosine on a calculator?
Set your calculator to the correct mode (degrees or radians), then press the cos button followed by the angle value. For example, to find cos(60°), set to degree mode and type cos(60).
What are common cosine values?
Common values: cos(0°) = 1, cos(30°) = √3/2 ≈ 0.866, cos(45°) = √2/2 ≈ 0.707, cos(60°) = 0.5, cos(90°) = 0.
What is the law of cosines?
The law of cosines extends the Pythagorean theorem to non-right triangles: c² = a² + b² - 2ab·cos(C), where C is the angle opposite side c. It is used to find sides or angles in any triangle.