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Value of Cos 2 pi

Value of Cos 2 pi

Value of cos2π

In this Trigonometric angle value based article, we have to find the Value of Cos 2 pi which is important for upcoming school and government level exams. In addition, The cosine of 2 pi (2π) or Value of Cos 2 pi is equal to 1. This can be seen from the unit circle, which is a circle with a radius of 1 centered at the origin of the coordinate plane. The unit circle is used to define the trigonometric functions for all angles, including those beyond the range of 0 to 90 degrees.

Value of Cos 2 pi : The cosine function is defined as the x-coordinate of the point on the unit circle that is at an angle of θ from the positive x-axis. In other words, the cosine of an angle θ is the horizontal distance from the origin to the point on the unit circle that is at an angle θ.

Cos 2pi Using Unit Circle
Cos 2pi Using Unit Circle

For the angle of 2 pi (2π) radians, the point on the unit circle is on the positive x-axis, which is the same as the point (1, 0). Therefore, the Value of Cos 2 pi (2π) is 1.

You can also verify this using the formula for the cosine function: cos θ = x/r, where x is the x-coordinate of the point on the unit circle, r is the radius of the circle (which is 1 in the case of the unit circle), and θ is the angle in radians.

Substituting the values for x, r, and θ, we have: cos 2π = 1/1

cos 2π = 1

Therefore, the Value of Cos 2 pi or cosine of 2 pi (2π) is 1.

Value of Cos pi

The cosine of pi (π) is equal to -1. This can be seen from the unit circle, which is a circle with a radius of 1 centered at the origin of the coordinate plane. The unit circle is used to define the trigonometric functions for all angles, including those beyond the range of 0 to 90 degrees.

The cosine function is defined as the x-coordinate of the point on the unit circle that is at an angle of θ from the positive x-axis. In other words, the cosine of an angle θ is the horizontal distance from the origin to the point on the unit circle that is at an angle θ.

Cos pi Using Unit Circle
Cos pi Using Unit Circle

For the angle of pi (π) radians, the point on the unit circle is on the negative x-axis, which is the same as the point (-1, 0). Therefore, the cosine of pi (π) is -1.

You can also verify this using the formula for the cosine function: cos θ = x/r, where x is the x-coordinate of the point on the unit circle, r is the radius of the circle (which is 1 in the case of the unit circle), and θ is the angle in radians.

Substituting the values for x, r, and θ, we have: cos π = (-1)/1

cos π = -1

Therefore, the cosine of pi (π) is -1.

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