Final answer:
The exact values of sinθ/2 and cosθ/2 for sinθ = 11/19 on the interval 0° ≤ θ ≤ 90° are: Sinθ/2: ±(2/√19), Cosθ/2: ±(√15/√19).
Step-by-step explanation:
To find the exact values of sinθ/2 and cosθ/2 for sinθ = 11/19 on the interval 0° ≤ θ ≤ 90°, we can use the half-angle identities for sine and cosine.
The half-angle identity for sine is: sin(θ/2) = ±√((1 - cosθ)/2)
The half-angle identity for cosine is: cos(θ/2) = ±√((1 + cosθ)/2)
Since sinθ = 11/19, we can substitute this value into the half-angle identities to find sin(θ/2) and cos(θ/2).
sin(θ/2) = ±√((1 - cosθ)/2) = ±√((1 - 11/19)/2) = ±√(8/38) = ±√(4/19) = ±(2/√19)
cos(θ/2) = ±√((1 + cosθ)/2) = ±√((1 + 11/19)/2) = ±√(30/38) = ±√(15/19) = ±(√15/√19)
Therefore, the exact values of sinθ/2 and cosθ/2 for sinθ = 11/19 on the interval 0° ≤ θ ≤ 90° are:
Sinθ/2: ±(2/√19)
Cosθ/2: ±(√15/√19)