From the trigonometry we should know that
sin² θ + cos² θ = 1
∴ cos² θ = 1 - sin² θ
given that ⇒⇒⇒ sin θ = 1/4
∴ cos² θ = 1 - sin² θ = 1 - (1/4)² = 0.9375
∴ cos θ = √0.9375 = 0.968 or -0.968
but sin θ is positive and tan θ positive because tan θ > 0 as stated in the problem
So, cos θ should be positive
∴ cos θ = 0.968
