Express the exact value of csc 60 degrees with a rational denominator.

csc 6 0 o = s in 6 0 o 1 ​ = 2 3 ​ ​ 1 ​ = 3 ​ 2 ​ = 3 ​ 2 ​ ⋅ 3 ​ 3 ​ ​ = 3 2 3 ​ ​

Answered by Anonymous | 2024-06-10

Note that the exact value of **csc 60° **with a rational denominator is (2√3)/3.
How to compute the above
The reciprocal identity states that csc(theta) = 1/sin(θ).
Since we know that sin 60 degrees = √3/2, we can substitute this value into the reciprocal identity -
csc 60° = 1/(√3/2).
To rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator -
csc 60°= (1/(√3/2)) * (√3/√3).
csc 60° = √3/(√3 * (√3/2)).
= √3/(√3 * √3/2).
= √3/(√9/2).
= √3/(3/2).
To **divide **by a fraction, we multiply by its **reciprocal **-
csc 60° = √3 * (2/3).
csc 60° = (2√3)/3.
So it is correct to state that , the exact value of csc 60° with a **rational denominator **is (2√3)/3.
Learn more about **rational denominator **at:
https://brainly.com/question/14261303
#SPJ6

Answered by azikennamdi | 2024-06-18

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Answered by azikennamdi | 2024-12-16