SOLUTION: Find the exact values of the six trigonometric functions of θ if θ is in standard position and the terminal side of θ is in the specified quadrant and satisfies the given condit

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Question 1148549: Find the exact values of the six trigonometric functions of θ if θ is in standard position and the terminal side of θ is in the specified quadrant and satisfies the given condition.
IV; on the line 3x + 5y = 0
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Equation of the line: 3x + 5y = 0 i.e. y = -(3/5)x
Slope of the line = -3/5
tan θ = -3/5 (negative since in Quadrant IV)
cot θ = 1/tan θ = 5/3

We know
cosec² □ - cot² θ = 1
cosec² θ = 1 + cot² θ
cosec θ = √(1 + cot² θ) = -√(1 + (5/3)²) = -√34/3
sin θ = 1/cosec θ = -3/√34
cos θ = √(1 - sin² θ) = √(1 - 9/34) = 5/√34
sec θ = 1/cos θ = √34/5