Question

If 4secθ = 5, find the value of sinθ​

Answer 1

sinθ = 3/5

Step-by-step explanation:

secθ = 5/4

cosθ = 4/5

sin^2θ + cos^2θ = 1

sin^2θ + (4/5)^2 = 1

sin^2θ = 1 - 16/25

sin^2θ = 25-16/25

sin^2θ = 9/25

sinθ = 3/5

Answer 2

Step-by-step explanation:

4Sec∅ = 5

=> Sec∅ = 5/4

Sec∅ = 1/Cos∅

=> Cos∅ = 4/5

Cos∅ = base / hypotenuse

4/5 = b/h

let the base be 4x and the hypotenuse be 5x because 4x/5x = 4/5.

By Pyth. Theorem

(hypotenuse)² = (Perpendicular)² + (base)²

(5x)² = p² + (4x)²

25x² = p² + 16x²

p² = 9x²

=> perpendicular = 3x

Sin∅ = Perpendicular/hypotenuse

Sin∅ = 3x/5x

=> Sin∅ = 3/5