Cos(2 pi) is equal to 1. The cosine function, cos(x), oscillates between 1 and -1 with a period of 2pi as x varies. By definition, cos(0) = 1, and the periodicity of the function means the cosine of all multiples of 2pi (2pi, 4pi and so on) is also equal to 1.

Which angle is pi?

The point is that pi radians is equal to 180 degrees. Radians are a unit of measurement for angles, just like degrees are, and pi is just the number of radians that makes up that angle. Just as one radian is equal to 57.3 degrees (approximately).

What is pie by 2?

chord: a line segment within a circle that touches 2 points on the circle. pi ( ): A number, 3.141592, equal to (the circumference) / (the diameter) of any circle. radius: distance from center of circle to any point on it. sector: is like a slice of pie (a circle wedge).

What is the value of cos 60?

Values of Trigonometric ratios for 0, 30, 45, 60 and 90 degrees. I have noticed that students cannot actually remember values of six trigonometric ratios (sin, cos, tan, cosec, sec and cot) for 0 , 30 , 45 , 60 and 90 .

Can you do sin of 90?

Specifically, the sine of an angle is defined as the y co-ordinate of the circle at that particular angle (see image above). So if you want to know what sin(90 degrees) is check the y- coordinate when the angle is 90, well since the radius of the circle is 1, this implies that sin90 is 1.

Why is tan 45 degrees equal to 1?

Draw the triangle and you will see that a = b. Tangent of 45 degrees is when both the opposite and adjacent sides of the 45 degree angle at origin are equal. A line at 45 degrees to the x-axis is also at 45 degrees to the y-axis because 45 degrees bisects the 90 degree angle between the two axes.

Why is the cosine of 90 0?

When x = 90°, we are talking about a right triangle with two right angles. This is only possible (only hypothetically) when the side opposite to x equals the hypotenuse and therefore the adjacent side becomes zero in length. Therefore, cosx becomes zero. Since in cos 90, base is 0, therefore therefore cos 90 is zero.

Is SEC hypotenuse over adjacent?

Likewise, the definition of cosine is represented by cah (cosine equals adjacent over hypotenuse), and the definition of tangent is represented by toa (tangent equals opposite over adjacent). That is, cosecant is the reciprocal of sine, secant is the reciprocal of cosine, and cotangent is the reciprocal of tangent.

Why is the tangent of 90 degrees undefined?

As our first quadrant angle increases, the tangent will increase very rapidly. As we get closer to 90 degrees, this length will get incredibly large. At 90 degrees we must say that the tangent is undefined (und), because when you divide the leg opposite by the leg adjacent you cannot divide by zero.

Is the tangent of 90 Infinity?

tan of 90 degrees is equal to the length of the opposite side divided by the length of the adjacent side. the infinity measurement expresses the fact that the tangent is undefined at 90 degrees.

What is tan 60 degrees as a fraction?

30 DegreesAngleTan=Sin/Cos30°1 √3 = √3 345°160°√3

What is the difference between a degree and radian?

The angles of a triangle, on the other hand, are equal to 180 degrees. The radius of a circle is one-half of the distance across its center which makes an angle equal to one radian. A radian is equal to 180 degrees because a whole circle is 360 degrees and is equal to two pi radians.

How do you find tan?

Example

Step 1 The two sides we know are Opposite (300) and Adjacent (400).

Step 4 Find the angle from your calculator using tan-1

What is tan to the negative 1?

The Value of the Inverse Tan of 1. As you can see below, the inverse tan-1 (1) is 45° or, in radian measure, Π/4. It is helpful to think of tangent as the ratio of sine over cosine, ie: . Therefore, tan(Θ) to equal 1, sin(Θ) and cos(Θ) must have the same value.

Can Tangent be less than 1?

The tangent ratio can be bigger than 1 (the other two cannot). If two right triangles are similar, then their sine, cosine, and tangent ratios will be the same (because they will reduce to the same ratio).

How is tangent the same as slope?

A tangent line is a straight line that touches a function at only one point. (See above.) The tangent line represents the instantaneous rate of change of the function at that one point. The slope of the tangent line at a point on the function is equal to the derivative of the function at the same point (See below.)

Can CSC be less than 1?

The cosecant is the reciprocal of the sine. Wherever the sine is positive but less than 1, the cosecant will be positive but greater than 1; wherever the sine is negative but greater than –1, the cosecant will be negative but less than –1.

Is SEC the same as 1 cos?

Secant, cosecant and cotangent, almost always written as sec, cosec and cot are trigonometric functions like sin, cos and tan. Note, sec x is not the same as cos-1x (sometimes written as arccos x). Remember, you cannot divide by zero and so these definitions are only valid when the denominators are not zero.

What is one over Secant?

The cotangent of x is defined to be the cosine of x divided by the sine of x: cot x = cos x sin x . The secant of x is 1 divided by the cosine of x: sec x = 1 cos x , and the cosecant of x is defined to be 1 divided by the sine of x: csc x = 1 sin x .

What is 1 cos?

(Math | Trig | Identities)sin(theta) = a / ccsc(theta) = 1 / sin(theta) = c / acos(theta) = b / csec(theta) = 1 / cos(theta) = c / btan(theta) = sin(theta) / cos(theta) = a / bcot(theta) = 1/ tan(theta) = b / a

What is cos over sin?

Each of the six trig functions is equal to its co-function evaluated at the complementary angle. Periodicity of trig functions. Sine, cosine, secant, and cosecant have period 2π while tangent and cotangent have period π. Identities for negative angles.

What is cos in trigonometry?

Sine, Cosine and Tangent are the main functions used in Trigonometry and are based on a Right-Angled Triangle. Before getting stuck into the functions, it helps to give a name to each side of a right triangle: “Opposite” is opposite to the angle θ “Adjacent” is adjacent (next to) to the angle θ

What is a theta in trigonometry?

In mathematics, the study of triangles is called trigonometry. Any unknown values of angles and sides may be discovered using the common trigonometric identities of Sine, Cosine and Tangent. Unknown angles are referred to as angle theta and may be calculated in various ways, based on known sides and angles.