moreIn 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.
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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 .
What is csc in terms of sin?
The cosecant ( csc ) (csc) (csc)
The cosecant is the reciprocal of the sine. It is the ratio of the hypotenuse to the side opposite a given angle in a right triangle.
Is csc sin or cos?
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/hyp | csc(q) = 1/sin(q) |
|---|---|
| cos(q) = adj/hyp | sec(q) = 1/cos(q) |
| tan(q) = sin(q)/cos(q) | cot(q) = 1/tan(q) |
What is the formula of csc?
For example, csc A = 1/sin A, sec A = 1/cos A, cot A = 1/tan A, and tan A = sin A/cos A.
How do you write cosecant?
Cosecant (csc) – Trigonometry function
In a right triangle, the cosecant of an angle is the length of the hypotenuse divided by the length of the opposite side. In a formula, it is abbreviated to just ‘csc’.
How do you find cosecant on the unit circle?
The cosecant function is the reciprocal of the sine function (cscx=1sinx) x = 1 sin . It can be found for an angle t by using the y -coordinate of the associated point on the unit circle: csct=1y t = 1 y . The cotangent function is the reciprocal of the tangent function (cotx=1tanx=costsint) x = 1 tan .
How do I know if I have SOH CAH TOA?
SOHCAHTOA is a mnemonic device helpful for remembering what ratio goes with which function.
- SOH = Sine is Opposite over Hypotenuse.
- CAH = Cosine is Adjacent over Hypotenuse.
- TOA = Tangent is Opposite over Adjacent.
What is the reciprocal of SEC?
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).
Is SEC the inverse of cos?
The secant function is a multiplicative inverse to the cosine function, which is defined off the zeroes of the cosine function. One of them, arccos, is the inverse function to cos. It reverses the operation. The other, sec, is 1cos, so it raises the results of the operation to the power of −1.
What is SEC formula?
Therefore, its basic formula is: sec X = frac{Hypotenuse}{Adjacent Side} Also, it is the reciprocal of the cosine value.
What is SEC Times csc?
Explanation: The Exp. =secxcscx. =1cosx1sinx. =sinxcosx.
How do you use cosecant?
The cosecant of an angle in a right triangle is a relationship found by dividing the length of the hypotenuse by the length of the side opposite to the given angle. This is the reciprocal of the sine function.
Is Sohcahtoa a trigonometry?
Sohcahtoa: SOHCAHTOA is a mnemonic device that is used in mathematics to remember the definitions of the three most common trigonometric functions.Sine, cosine, and tangent are the three main functions in trigonometry. They’re all based on ratios obtained from a right triangle.
Who discovered Sohcahtoa?
It was Leonhard Euler who fully incorporated complex numbers into trigonometry. The works of the Scottish mathematicians James Gregory in the 17th century and Colin Maclaurin in the 18th century were influential in the development of trigonometric series.
Can you use Sohcahtoa on any triangle?
Q: Is sohcahtoa only for right triangles? A: Yes, it only applies to right triangles.A: They hypotenuse of a right triangle is always opposite the 90 degree angle, and is the longest side.
Why is cosecant the reciprocal of sine?
Since sine function is the ratio of the lengths of the opposite side to the angle in consideration and hypotenuse in a right-angled triangle, the reciprocal of sine is the ratio of the hypotenuse and the opposite side of a right-angled triangle which is the formula for the cosecant function.
What is inverse of cosine?
The arccos function is the inverse of the cosine function. It returns the angle whose cosine is a given number.Means: The angle whose cosine is 0.866 is 30 degrees. Use arccos when you know the cosine of an angle and want to know the actual angle.