Question

csc 5 pie/3

Answer 1

[AI-generated answer — Bot GPT 3.5]

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.

Answer 2

5π/3 is in QIV, so csc(5π/3) = -2/√3

Answer 3

[AI-generated answer — Bot GPT 3.5]

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.