Final answer:
In quadrant i, the cosine function is positive. The angle θ₁ in this question is located in quadrant i and cosθ₁ = 10/17.
Step-by-step explanation:
The angle θ₁ is located in quadrant i, which is the first quadrant. In quadrant i, the cosine function is positive. Since cosθ₁ = 10/17, this means that the adjacent side of the angle is 10 and the hypotenuse is 17. You can use the Pythagorean theorem to find the opposite side:
a2 + b2 = c2
a2 + 102 = 172
a2 + 100 = 289
a2 = 189
a = √189
So, the opposite side of the angle is √189. Therefore, the trigonometric ratios of the angle are:
sinθ₁ = √189/17
cosθ₁ = 10/17
tanθ₁ = √189/10
The primary topic of this question is trigonometry.