Final answer:
The values of secant, cosecant, and cotangent for 8π/3 are -2, -2√3/3, and √3 respectively.
Step-by-step explanation:
The trigonometric functions secant, cosecant, and cotangent can be determined using the values of sine, cosine, and tangent. First, let's find the values of sine, cosine, and tangent for 8π/3:
- Sine (sin) = sin(8π/3) = -√3/2
- Cosine (cos) = cos(8π/3) = -1/2
- Tangent (tan) = tan(8π/3) = (√3)/3
Now we can find the values of secant, cosecant, and cotangent:
- Secant (sec) = 1/cos(8π/3) = -2
- Cosecant (csc) = 1/sin(8π/3) = -2√3/3
- Cotangent (cot) = 1/tan(8π/3) = √3