if p(x,y) is the point on the unit circle defined by real number theta, then csc theta= _____. a. x/y. b. y/x. c. 1/x. d. 1/y.
Answer:
Option d is correct
\(Csc \ \theta =\frac{1}{y}\)
Step-by-step explanation:
Here P(x,y) is the point on unit circle ( unit circle has radius 1 and center (0,0))
Now in a diagram we can see that
OA= x
AP= y
radius OP =1
∠POA =θ
Now in ΔAOP
\(Csc\ \theta =\frac{hypotenuse }{opposite \ side} \\Csc\ \theta =\frac{OP}{AP}\)
\(Csc \ \theta =\frac{1}{y}\) ( since OP =1 and AP =y)