For csc θ = 8/5 and cot θ > 0, the trigonometric function values are sin θ = 5/8, cos θ = 3/8, tan θ > 0, cot θ = 8/5, sec θ = 8/3, and csc θ = 8/5.
Given csc θ = 8/5 and cotθ> 0 , evaulate the 6 trigonomeric functions of θ.
Firstly, since csc θ = 8/5, we know that sin θ = 5/8 (reciprocal of csc).
Next, as cot θ > 0, we find that tan θ > 0 (since cot θ = 1/tan θ).
Now, we can use the known values of sin θ and tan θ to compute the other trigonometric functions:
cos θ = sqrt(1 - sin^2 θ) = sqrt(1 - (5/8)^2) = 3/8
sec θ = 1/cos θ = 1/(3/8) = 8/3
cot θ = 1/tan θ = 1/(5/8) = 8/5
Now, we have all the trigonometric function values:
sin θ = 5/8, cos θ = 3/8, tan θ > 0, cot θ = 8/5, sec θ = 8/3, csc θ = 8/5.