Help!
sin B = ( 5 square root 2)/ (5 square root 3), find the value of csc B
since cscB = 1/sinB
cscB = 1/(5√2/5√3)
= 5√3/5√2 = √3/√2
That is what I have but those aren't my answer choices.
a. 2/�ã3
b. �ã6/3
c. -�ã6/2
d. �ã6/2
Which one would it be?
They obviously rationalized by answer
√3/√2
= √3/√2 *(√2/√2) = √6/2
Since the original given information was not rationalized I logically assumed they would supply the answer in the same way.
You could have used your calculator to evaluate my answer, then checked with of the given ones match it.
To find the value of csc B, we need to use the reciprocal relationship between sin and csc. The reciprocal of sin B is csc B, so we can find csc B by taking the reciprocal of sin B.
Given that sin B = (5√2) / (5√3), we can simplify it by multiplying the numerator and denominator by the conjugate of the denominator, which is (5√3):
sin B = (5√2) / (5√3) * (5√3) / (5√3)
This simplifies to:
sin B = (25√6) / (25√9)
The term √9 simplifies to 3, so we have:
sin B = (25√6) / (25 * 3)
Now we cancel out the common factor of 25:
sin B = √6 / 3
Finally, we can find the value of csc B by taking the reciprocal of sin B:
csc B = 1 / sin B
Plugging in the value of sin B:
csc B = 1 / (√6 / 3)
To divide by a fraction, we can multiply by the reciprocal:
csc B = 1 * (3 / √6)
Simplifying further:
csc B = 3 / √6
This is the simplified value of csc B.