Final answer:
a) sin(6/5π) = -1/2, b) cos(3/8π) = √2/2, c) cot(4/7π) = -√3/3, d) sec(6/11π) = -2/√3, e) csc(2/7π) = 2
Step-by-step explanation:
a) To find the exact value of sin(6/5π), we can use the unit circle. At 6/5π, the point on the unit circle will be (-√3/2, -1/2). Therefore, sin(6/5π) = -1/2.
b) To find the exact value of cos(3/8π), we can again use the unit circle. At 3/8π, the point on the unit circle will be (√2/2, √2/2). Therefore, cos(3/8π) = √2/2.
c) To find the exact value of cot(4/7π), we can use the fact that cot(θ) = 1/tan(θ). Therefore, cot(4/7π) = 1/tan(4/7π). To find tan(4/7π), we can use the unit circle. At 4/7π, the point on the unit circle will be (√3/2, -1/2). Therefore, tan(4/7π) = -√3/3. So cot(4/7π) = 1/(-√3/3) = -√3/3.
d) To find the exact value of sec(6/11π), we can again use the unit circle. At 6/11π, the point on the unit circle will be (-√3/2, 1/2). Therefore, sec(6/11π) = 1/(cos(6/11π)) = 1/(-√3/2) = -2/√3.
e) To find the exact value of csc(2/7π), we can use the fact that csc(θ) = 1/sin(θ). Therefore, csc(2/7π) = 1/sin(2/7π). To find sin(2/7π), we can use the unit circle. At 2/7π, the point on the unit circle will be (√3/2, 1/2). Therefore, sin(2/7π) = 1/2. So csc(2/7π) = 1/(1/2) = 2.