Cosine Triangle
Calculate the cosine of any angle in degrees using the formula cos(theta) = adjacent/hypotenuse. Free online trigonometry calculator with instant results for students, engineers, and professionals.
About This Calculator
The Cosine Calculator computes the trigonometric cosine function cos(theta) for any angle entered in degrees. Cosine is one of the six fundamental trigonometric functions and is defined as the ratio of the adjacent side to the hypotenuse in a right triangle. On the unit circle, cos(theta) represents the x-coordinate of a point at angle theta from the positive x-axis.
Cosine is an even, periodic function with period 360 deg (2pi radians). Its values range from -1 to 1, making it essential for describing oscillatory and wave phenomena. Key values include cos(0 deg) = 1, cos(45 deg) ≈ 0.7071, cos(60 deg) = 0.5, and cos(90 deg) = 0.
This calculator is used by students learning trigonometry, engineers analyzing forces and structures, physicists studying wave motion and harmonic oscillators, computer graphics developers calculating lighting and rotations, and professionals in fields requiring angle-based calculations.
Frequently Asked Questions
What is cosine in trigonometry?
Cosine (cos) is a fundamental trigonometric function that relates an angle of a right triangle to the ratio of the adjacent side to the hypotenuse. In a right triangle with angle theta, cos(theta) = adjacent side / hypotenuse. It is one of the six basic trigonometric functions.
How do you calculate cosine of an angle?
To calculate cos(theta), divide the length of the side adjacent to angle theta by the length of the hypotenuse. Alternatively, use the unit circle: cos(theta) is the x-coordinate of the point on the unit circle at angle theta from the positive x-axis.
What are common cosine values?
Common values: cos(0 deg) = 1, cos(30 deg) = sqrt3/2 ≈ 0.8660, cos(45 deg) = sqrt2/2 ≈ 0.7071, cos(60 deg) = 1/2 = 0.5, cos(90 deg) = 0, cos(180 deg) = -1. Cosine is an even function: cos(-theta) = cos(theta).
What is the range of the cosine function?
The cosine function outputs values between -1 and 1 inclusive for all real inputs. It is periodic with period 360 deg (2pi radians). The function decreases from 1 at 0 deg to -1 at 180 deg, then increases back to 1 at 360 deg.
Where is cosine used in real-world applications?
Cosine is used extensively in physics (calculating forces, wave motion, harmonic oscillation), engineering (structural analysis, signal processing), computer graphics (3D rotations, lighting calculations), navigation (GPS coordinates), and electrical engineering (AC circuit analysis).
What is the relationship between cosine and sine?
Cosine and sine are related by the Pythagorean identity: cos^2(theta) + sin^2(theta) = 1. They are also phase-shifted: cos(theta) = sin(theta + 90 deg). The derivative of sin(theta) is cos(theta), and the derivative of cos(theta) is -sin(theta).