I need help with this proof.....its due tomorrow?

Question

Prove that csc 0 is undefined

&

A sector of a circle has a central angle of D degrees. Prove that the area of the sector is A=(1/2)r^2R where r is the radius and Ris the Radian Measure


Thank you

Answer 1

csc(0)
= 1 / [sin(0)]
= 1 / 0
= undefined with 0 in denominator

Answer 2

A sector of a circle has a central angle of D degrees. Prove that the area of the sector is A=(1/2)r^2R where r is the radius and Ris the Radian Measure

usually we call the Radian measure, theta: the angle in radians.
The circle has an area equal to Pi r^2 and covers an angle of 2Pi. Using
proportions, the area of the circle is to the angle 2Pi as the area of the sector
A is to R (in your notation which is the angle). That is,

(Pi r^2)/(2Pi) = A/R
A = R (r^2)/2

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This can be proven using integrals to find the area of a sector of a circle.

Answer 3

Since Csc(0) is:
1/Sin(0) which is:
1/0, which is infinity, then,
Csc(0) is infinity!
If it were 0/0 or infinity/infinity, then it would be undefined.
PS: How does one get the symbol for infinity to paste into this area?

Answer 4

csc = 1 / sin

Since sin ( 0 ) = 0 and division by zero is undefined, csc ( 0 ) is undefined.

Sorry, I don't understand your second problem.