If csc theta = square root of 5 divided by 15, find sin theta
csc Ø = √5/15
then sinØ = 15/√5 which is greater than 1, thus impossible.
error in the question!
To find sin(theta) given csc(theta), we can use the reciprocal relationship between sine and cosecant.
The cosecant function is the reciprocal of the sine function, meaning that csc(theta) = 1 / sin(theta).
In this case, we are given that csc(theta) = √5 / 15.
To find sin(theta), we can reciprocate csc(theta):
1 / csc(theta) = sin(theta).
Substituting the value of csc(theta):
1 / (√5 / 15) = sin(theta).
To simplify this expression, we multiply the numerator and denominator of the fraction by the conjugate of the denominator (√5 / 15):
1 / (√5 / 15) * (√5 / 15) = sin(theta).
This simplifies to:
15 / √5 = sin(theta).
However, it is common practice to rationalize the denominator, so we can multiply the numerator and denominator by √5:
(15 / √5) * (√5 / √5) = sin(theta).
This yields:
(15 * √5) / 5 = sin(theta).
Simplifying further:
3√5 = sin(theta).
Therefore, sin(theta) is equal to 3√5.