Verified answer

Given that the angle is positive and acute, you know the angle is in the first quadrant, 0 < Θ < 90° where all the trigonometric functions are positive. You are given that cosΘ is √3/4 and are asked for the exact value of sinΘ.

From the Pythagorean Identity, you know that sin²Θ + cos²Θ = 1, from which:

sin²Θ = 1-cos²Θ

or

sinΘ = √(1-cos²Θ)

The positive value of the square root is chosen because we've already found that the value of the sine is positive since the angle Θ is in the first quadrant.

sinΘ = √[1-(√3/4)²] = √(1-3/16) = √(13/16) = √13/4

in accordance to the undertaking, x is a good acute perspective. as a result, all of us understand that it may merely be in Quadrant I. cos (x) = ?3 / 4 bear in techniques cos = adj / hyp on a real triangle. The opp factor of perspective x could be chanced on utilising Pythagorean Theorem. a² + b² = c² (?3)² + b² = 4² 3 + b² = sixteen b² = 13 b = ?13 bear in techniques sin = opp / hyp. The opp we chanced directly to be is ?13 and the hyp is 4. sin (x) = ?13 / 4