Questions: Find the exact value of each of the remaining trigonometric functions of θ. sin θ = 5/13, θ in Quadrant II sec θ = csc θ =

Solution Steps

Since sin θ = 5/13 and θ is in Quadrant II, we know that cos θ will be negative. We can use the Pythagorean identity: sin²θ + cos²θ = 1.

(5/13)² + cos²θ = 1

25/169 + cos²θ = 1

cos²θ = 1 - 25/169

cos²θ = 144/169

cos θ = -√(144/169) (negative because θ is in Quadrant II)

cos θ = -12/13

sec θ is the reciprocal of cos θ:

sec θ = 1/cos θ = 1/(-12/13) = -13/12

csc θ is the reciprocal of sin θ:

csc θ = 1/sin θ = 1/(5/13) = 13/5

Final Answer