To convert the angle from radians to degrees, you can multiply by 180/π.
So, csc(5π/3) = 1 / sin(5π/3)
Using the unit circle, we find that sin(5π/3) = sin(π/3) = √3/2.
Therefore, csc(5π/3) = 1 / (√3/2) = 2/√3.
To rationalize the denominator, we multiply both the numerator and denominator by √3:
csc(5π/3) = (2/√3) * (√3/√3) = 2√3 / 3.
So, csc(5π/3) is equal to 2√3 / 3.
csc 5 pie/3
3 answers
5π/3 is in QIV, so csc(5π/3) = -2/√3
My apologies for the mistake. You are correct.
Since 5π/3 is in Quadrant IV, the value of csc(5π/3) should be negative.
To find the value, we can use the fact that csc(theta) is the reciprocal of sin(theta).
sin(5π/3) = sin(π/3) = √3/2.
Thus, csc(5π/3) = 1 / sin(5π/3) = 1 / (√3/2) = 2/√3.
Multiplying both the numerator and denominator by √3, we get:
csc(5π/3) = (2/√3) * (√3/√3) = 2√3 / 3.
Therefore, csc(5π/3) = -2√3 / 3 in Quadrant IV.
Since 5π/3 is in Quadrant IV, the value of csc(5π/3) should be negative.
To find the value, we can use the fact that csc(theta) is the reciprocal of sin(theta).
sin(5π/3) = sin(π/3) = √3/2.
Thus, csc(5π/3) = 1 / sin(5π/3) = 1 / (√3/2) = 2/√3.
Multiplying both the numerator and denominator by √3, we get:
csc(5π/3) = (2/√3) * (√3/√3) = 2√3 / 3.
Therefore, csc(5π/3) = -2√3 / 3 in Quadrant IV.