What is the cosine for an angle that has a sine of 4/17√ and is in Quadrant I? Use the Pythagorean identity sin2(θ)+cos2(θ)=1 and the quadrant to solve.(1 point) Responses 117 Start Fraction 1 over 17 End Fraction 117√ Start Fraction 1 over Start Root 17 End Root End Fraction −117 negative Start Fraction 1 over 17 End Fraction −117√
We know that the sine of the angle is given as 4/17√ and that the angle is in Quadrant I.
Using the Pythagorean identity sin²(θ) + cos²(θ) = 1, we can find the value of the cosine.
Since the angle is in Quadrant I, both the sine and cosine are positive.
Let's calculate the value of the cosine:
sin²(θ) + cos²(θ) = 1
(4/17√)² + cos²(θ) = 1
(16/289) + cos²(θ) = 1
cos²(θ) = 1 - 16/289
cos²(θ) = 273/289
cos(θ) = √(273/289)
cos(θ) = √273/√289
cos(θ) = √273/17
Therefore, the cosine for the angle with a sine of 4/17√ and in Quadrant I is:
cos(θ) = √273/17.