csc theta = (sqr root 5) over 15, find sine theta
csc = 1/sin or 1/csc = sin
15/ sqrt 5
multiply numerator and denominator by sqrt of 6
15 sqrt 5 divided by 5
reduces to 3 sqrt 5
same bogus question. csc(theta) cannot be less than 1.
To find the value of sine theta, we will use the trigonometric identity that relates sine and cosine:
sin^2(theta) + cos^2(theta) = 1
First, let's find the value of cosine theta by using the given information. We are given that csc theta is equal to the square root of 5 over 15. The reciprocal of csc theta is sin theta:
csc theta = 1/sin theta
Therefore, we can rewrite the given equation as:
1/(sin theta) = √5/15
To solve for sin theta, we will take the reciprocal of both sides:
sin theta = 1 / (√5/15)
Since dividing by a fraction is the same as multiplying by its reciprocal, we can simplify:
sin theta = 1 * (15/√5)
Now, to simplify further, we will rationalize the denominator (√5) by multiplying both the numerator and denominator by √5:
sin theta = (15/√5) * (√5/√5)
This simplifies to:
sin theta = 15√5 / 5
Finally, we can further simplify by canceling out the common factor of 5:
sin theta = 3√5
Therefore, sin theta is equal to 3 times the square root of 5.