If sin θ = 12/13, and θ is in quadrant 3, what is the value of cos θ?

Question

1. -13/5
2. -5/13
3. 13/5
4. 5/13

Answer 1

sin in the 3rd quadrant is negative. Maybe a typo?

sin = opposite/hypotenuse = -12/13

Use the Pythagorean theorem to find the adjacent side needed for cos

√13²-(-12)² = 5 The 3rd quadrant means this must be -5

cos Θ = adjacent/hypotenuse

cos Θ = -5/13