What is the range of a cosecant function?
The range of the function is y≤−1 or y≥1 . The graph of the cosecant function looks like this: The domain of the function y=csc(x)=1sin(x) is all real numbers except the values where sin(x) is equal to 0 , that is, the values πn for all integers n . The range of the function is y≤−1 or y≥1 .
What is the cosecant of an angle?
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.
What are the values of special angles?
TRIGONOMETRIC VALUES OF SPECIAL ANGLES
| angle/number | sine sin=OPPHYP | cotangent (reciprocal of tangent) |
|---|---|---|
| 30∘=π6 rad | 12 | √3 |
| 45∘=π4 rad | 1√2=√22 | 1 |
| 60∘=π3 rad | √32 | 1√3=√33 |
| 90∘=π2 rad | 1 | 0 (cot:=cossin cot := cos sin ) |
What is the value of csc 45?
Trigonometry Examples The exact value of csc(45°) csc ( 45 ° ) is √2 .
What angles are not in the domain of the cosecant function?
The cosecant function will be defined as long as the sine value is not 0. Therefore the domain of the cosecant function excludes all angles with sine value 0, which are \begin{align*}0^\circ\end{align*}, \begin{align*}180^\circ\end{align*}, \begin{align*}360^\circ\end{align*}, etc.
What is the formula of cosecant function?
The cosecant function formula can be written in two different ways: csc x = 1/sin x. csc x = Hypotenuse/Perpendicular OR Hypotenuse/Opposite Side.
What is the value of Cosec 90 degree?
1
The value of cosec 90 degrees is 1. Cosec 90 degrees can also be expressed using the equivalent of the given angle (90 degrees) in radians (1.57079 . . .).
What is the value of csc 60?
Trigonometry Examples The exact value of csc(60°) csc ( 60 ° ) is 2√3 . Multiply 2√3 by √3√3 .
What is the value of csc 30?
Trigonometry Examples The exact value of csc(30°) csc ( 30 ° ) is 2 .
What is the restricted domain of csc?
The domains of cosecant and secant are restricted — you can only use the functions for angle measures with output numbers that exist.
How do you find the domain of a Cscx?
The domain of y=csc(x) is every value in the domain of sine with the exception of where sin(x)=0 , since the reciprocal of 0 is undefined. So we solve sin(x)=0 and get x=0+π⋅n where n∈Z . That means the domain of y=csc(x) is x∈R,x≠π⋅n , n∈Z .
What angle is csc undefined?
zero degrees
In fact, the value returned by the cosecant function for an angle of either zero degrees or one hundred and eighty degrees is considered to be undefined, since the equation csc (θ ) = 1/sin (θ ) will involve division by zero.
What does cosecant mean in math?
Math Open Reference. 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’. Of the six possible trigonometric functions, cosecant, cotangent, and secant, are rarely used.
What are the trigonometric function values of special angles?
Trigonometric Function Values Of Special Angles. How to derive the trigonometric function values of 30, 45 and 60 degrees and their corresponding radian measure. Cofunction identities are also discussed: sin θ = cos (90° – θ) cos θ = sin (90° – θ) Show Video Lesson.
The cosecant of an angle is defined with respect to the sides of a right triangle. In a right triangle, the cosecant is equal to the length of the hypotenuse divided by the side opposite the angle. The cosecant is the reciprocal function of the sine. Here, we will learn more about the cosecant and use diagrams to facilitate understanding.
What is the cosecant function in trigonometry?
We have 6 ratios in trigonometry. The cosecant function is the ratio of the hypotenuse to the opposite side in a right angled triangle. θ = opposite side hypotenuse, we derive the cosecant equation as follows. Consider the 45-45-45 triangle and 30-60-90 triangle and let’s determine the cosecant function of the angles.