Use enough parentheses for this to be correct.veganazi said:Homework Statement
csc^-1(2sqrt3/3)
Homework Equations
csc^-1(2sqrt3/3) = sin^-1(3/2sqrt3)
The Attempt at a Solution
My Math Lab says I am supposed to use the equivalent sine function, so then I got sin^-1(3/2sqrt3). Then what do I do?
The cosecant function is defined as the reciprocal of the sine function, or 1 divided by the sine of an angle. It is denoted as csc(x) or cosec(x).
The domain of the cosecant function is all real numbers except for the values where the sine function is equal to 0, which are the multiples of π. The range of the cosecant function is all real numbers except for 0.
The cosecant function can be visualized on the unit circle as the vertical distance from the point on the circle to the x-axis. It is also the reciprocal of the y-coordinate of the point on the unit circle.
To find the exact value of the cosecant function, you can use the Pythagorean identity, which states that csc²(x) = 1 + cot²(x). You can also use the trigonometric ratios for special angles such as 30°, 45°, and 60°.
Yes, the cosecant function can be negative, as it is the reciprocal of the sine function. The sine function is positive in the first and second quadrants, and negative in the third and fourth quadrants. Therefore, the cosecant function will also be positive in the first and second quadrants, and negative in the third and fourth quadrants.