Quick Answer: What Is CSC In Terms Of Sin?

What is tan theta in terms of sin and cos?

Explanation: tanθ=sinθcosθ = sinθ√cos2θ = sinθ√1−sin2θ.

Where does sin equal?

Always, always, the sine of an angle is equal to the opposite side divided by the hypotenuse (opp/hyp in the diagram).

What quadrant is sin inverse?

The arcsine of a positive number is a first quadrant angle, sin-1(+) is in quadrant I. The arcsine of zero is zero, sin-1(0) is 0. The arcsine of a negative number is a negative first quadrant angle, sin-1(-) is in quadrant -I, a clockwise-angle of less than or equal to – /2.

What is the CSC in math?

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 sin 1 called?

Other Names. Sometimes sin-1 is called asin or arcsin. Likewise cos-1 is called acos or arccos. And tan-1 is called atan or arctan.

What is Cotangent the inverse of?

In trigonometry, the trigonometric functions are obtained from the ratios of the sides of a right-angle triangle. The six important trigonometric ratios are sine, cosine, tangent, cosecant, secant and cotangent. … The inverse of the cotangent function is called inverse cotangent or arccot. It is denoted by cot-1x.

What is Sinπ?

The exact value of sin 180 is zero. Sine is one of the primary trigonometric functions which helps in determining the angle or sides of a right-angled triangle. It is also called trigonometric ratio.

Is cot the inverse of tan?

cot(x) = 1/tan(x) , so cotangent is basically the reciprocal of a tangent, or, in other words, the multiplicative inverse. arctan(x) is the angle whose tangent is x.

What is the value of sin 1 1?

The inverse sin of 1, i.e., sin-1 (1) is a very unique value for the inverse sine function. Sin-1(x) will give us the angle whose sine is x. Hence, sin-1 (1) is equal to the angle whose sine is 1. Since the inverse sin-1 (1) is 90° or Π/2.

What is the value of sin 1 0?

The answer isn’t limited to a range of values, so the exact value is: sin−1(0)=nπ where n is an integer – this allows us to express not just 0 degrees but also π,2π,3π,−π,−2π and so on.

What does sin to the negative 1 mean?

The inverse sin of 1, ie sin-1 (1) is a very special value for the inverse sine function. Remember that sin-1(x) will give you the angle whose sine is x . Therefore, sin-1 (1) = the angle whose sine is 1.

What does CSC graph look like?

The vertical asymptotes of cosecant drawn on the graph of sine. … The cosecant goes down to the top of the sine curve and up to the bottom of the sine curve. After using the asymptotes and reciprocal as guides to sketch the cosecant curve, you can erase those extra lines, leaving just y = csc x.

What is Arcsin equal to?

The arcsin function is the inverse of the sine function. It returns the angle whose sine is a given number….arcsin.sin30 = 0.5Means: The sine of 30 degrees is 0.5arcsin 0.5 = 30Means: The angle whose sin is 0.5 is 30 degrees.

Does sin 1 equal CSC?

Sine of an angle is the side of the triangle that does not touch the angle divided by the hypotenuse. … cosecant is the reciprical of the sin function or 1/sin(x) so that csc(x)*sin(x) = 1 when it is defined. The two can be confused since arcsin(x) is often denoted as sin^-1(x) and x^-1 is 1/x.

Is sin 1 the same as 1 sin?

The notation sin-1(x) has been misunderstood to mean 1/sin(x). … So sin-1(x) means the inverse sine of x, that is, the function that undoes the sine function. It is not equal to 1/sin(x).

Is sin a CSC or SEC?

The functions are usually abbreviated: sine (sin), cosine (cos), tangent (tan) cosecant (csc), secant (sec), and cotangent (cot)….Math2.org Math Tables:sin(q) = opp/hypcsc(q) = 1/sin(q)cos(q) = adj/hypsec(q) = 1/cos(q)tan(q) = sin(q)/cos(q)cot(q) = 1/tan(q)

How many trig identities are there?

36 Trig IdentitiesThe 36 Trig Identities You Need to Know. If you’re taking a geometry or trigonometry class, one of the topics you’ll study are trigonometric identities.

Why is it called Arcsin?

If you have a numerical value and you want the size of the angle whose sine has this value, you get something like this, where the value is a number and the arcsin is expressed in degrees of arc. It essentially reverses the process of the sine function. … It is called “arcsin” because it gives you a measure of the arc.

What is the reciprocal of sin theta?

The reciprocal cosine function is secant: sec(theta)=1/cos(theta). The reciprocal sine function is cosecant, csc(theta)=1/sin(theta). The reciprocal tangent function is cotangent, expressed two ways: cot(theta)=1/tan(theta) or cot(theta)=cos(theta)/sin(theta).

What are the six trigonometric functions?

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.

How do you convert sin to Tangent?

To rewrite the sine function in terms of tangent, follow these steps:Start with the ratio identity involving sine, cosine, and tangent, and multiply each side by cosine to get the sine alone on the left.Replace cosine with its reciprocal function.Solve the Pythagorean identity tan2θ + 1 = sec2θ for secant.More items…

What is tan theta formula?

Tan x formula The Tan Θ is the ratio of the Opposite side to the Adjacent, where (Θ) is one of the acute angles. Tan \Theta = \frac{Opposite Side}{Adjacent Side}

What is CSC equal to?

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 .

Is inverse sine the same as CSC?

Inverse Reciprocal Trigonometric Functions We already know that the cosecant function is the reciprocal of the sine function. This will be used to derive the reciprocal of the inverse sine function. Because cosecant and secant are inverses, \begin{align*}\sin^{-1} \frac{1}{x} = \csc^{-1} x\end{align*} is also true.

What is the formula for CSC?

Cosecant, Secant and CotangentCosecant Function:csc(θ) = Hypotenuse / OppositeSecant Function:sec(θ) = Hypotenuse / AdjacentCotangent Function:cot(θ) = Adjacent / Opposite

What is the opposite of CSC?

Finding the cosecant We know that the cosecant is the reciprocal of the sine. Since sine is the ratio of the opposite to the hypotenuse, cosecant is the ratio of the hypotenuse to the opposite.

What is the inverse of sine called?

The inverse is used to obtain the measure of an angle using the ratios from basic right triangle trigonometry. … The inverse of sine is denoted as Arcsine or on a calculator it will appear as asin or sin-1.