how would I know what csc 450 degrees ?
I know that csc is hypotenuse over opposite, but then when I graph this the opposite is the hypotenuse so how am i supposed to solve it?
To find the value of csc 450 degrees, we can start by understanding the trigonometric functions within a unit circle. The definition of csc (cosecant) is the reciprocal of sin (sine).
In a unit circle, sin(theta) = opposite/hypotenuse, and csc(theta) = 1/sin(theta). To find the value of csc 450 degrees, we need to consider that 450 degrees is in the second quadrant of the unit circle where the y-coordinate (opposite) is positive and the x-coordinate (hypotenuse) is negative.
Here's the step-by-step process to find csc 450 degrees:
1. Convert 450 degrees to radians: Multiply by π/180 to convert degrees to radians. 450 degrees * π/180 = 5π/2 radians.
2. Draw a unit circle: Represent the unit circle on a graph with the center at (0, 0) and a radius of 1 unit.
3. Locate the angle: Move counterclockwise on the unit circle until reaching an angle of 5π/2 radians or 270 degrees.
4. Identify the coordinates: The coordinates at 5π/2 radians or 270 degrees are (-1, 0).
5. Calculate sine: The sine of 5π/2 radians or 270 degrees is 0 because the y-coordinate (opposite) is 0.
6. Calculate cosecant: The cosecant of 5π/2 radians or 270 degrees is the reciprocal of sine, which is undefined because it is dividing by zero. Therefore, csc 450 degrees is undefined.
So, csc 450 degrees is undefined because the sine of 5π/2 radians or 270 degrees is equal to zero, and the cosecant function is undefined when dividing by zero.
Keep in mind that csc (θ) = 1/sin(θ), and if sin(θ) equals zero, then csc(θ) is undefined.