Quick Answer: What Is A Reciprocal Identity In Trig?

What is CSC of an angle?

In a right angled triangle, the cosecant of an angle is: The length of the hypotenuse divided by the length of the side opposite the angle.

The abbreviation is csc.

csc θ = hypotenuse / opposite..

What is the reciprocal identity?

In general, the reciprocal identities are identities in which the equality relation occurs by swapping or interchanging the numerator and the denominator of the number. … Trigonometric functions: Consider the first quadrant with the terminate point of radius r is P(x, y).

What is a reciprocal trig function?

There are three reciprocal trigonometric functions, making a total of six including cosine, sine, and tangent. The reciprocal cosine function is secant: sec(theta)=1/cos(theta). The reciprocal sine function is cosecant, csc(theta)=1/sin(theta). … Cosecant theta is 1 over y and cotangent is x over y.

What is the reciprocal of sin θ?

The reciprocal identity of sin θ must be equal to 1/sin θ, since that is the number that, when multiplied by sin θ, produces 1. The same is true for cos θ and tan θ. Mathematicians give these reciprocals the names cosecant, secant and cotangent respectively.

What is the reciprocal of Cotangent?

Cosecant is the reciprocal of sine. Secant is the reciprocal of cosine. Cotangent is the reciprocal of tangent.

What does R mean in trigonometry?

When you work with angles in all four quadrants, the trig ratios for those angles are computed in terms of the values of x, y, and r, where r is the radius of the circle that corresponds to the hypotenuse of the right triangle for your angle.

Is CSC the same as sin 1?

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 are the 3 trigonometric identities?

The three main functions in trigonometry are Sine, Cosine and Tangent. That is our first Trigonometric Identity.

What are the 6 reciprocal identities?

Terms in this set (6)sin. 1/csc.cos. 1/sec.tan. 1/cot.cot. 1/tan.sec. 1/cos.csc. 1/sin.

Is the value of sin 60?

The exact value of sin(60°) sin ( 60 ° ) is √32 .

What are the 2 quotient identities?

In trigonometry, quotient identities refer to trig identities that are divided by each other. There are two quotient identities that are crucial for solving problems dealing with trigs, those being for tangent and cotangent. Cotangent, if you’re unfamiliar with it, is the inverse or reciprocal identity of tangent.

What are the 6 trig ratios?

There are six trigonometric ratios, sine, cosine, tangent, cosecant, secant and cotangent. These six trigonometric ratios are abbreviated as sin, cos, tan, csc, sec, cot.

Why is Cosecant the reciprocal of sine?

If you take a look at the unit circle, the secant is the distance from the center to the vertical tangent in a certain direction. Defined this way, the secant is the reciprocal of the cosine. Logically, its complement was called the cosecant, which is the reciprocal of the sine.