sin theta = 12/13, theta in quadrant II

sin theta = 12/13, theta in quadrant II We are given that sin(θ) = 12/13, and θ is in quadrant II. Step 1: Recall the identity for the sine function. sin(θ) = opposite / hypotenuse Here, sin(θ) = 12/13, so the opposite side is 12 and the hypotenuse is 13. Step 2: Use the Pythagorean theorem to find the adjacent side. We know: opposite^2 + adjacent^2 = hypotenuse^2 12^2 + adjacent^2 = 13^2 144 + adjacent^2 = 169 adjacent^2 = 169 - 144 adjacent^2 = 25 adjacent = 5 Step 3: Determine the sign of the adjacent side. Since θ is in quadrant II, the adjacent side is negative. Therefore, the adjacent side is -5. Step 4: Use the identity for cosine to find cos(θ). cos(θ) = adjacent / hypotenuse cos(θ) = -5 / 13 Step 5: Use the identity for tangent to find tan(θ). tan(θ) = opposite / adjacent tan(θ) = 12 / (-5) tan(θ) = -12/5 Final answers: cos(θ) = -5/13 tan(θ) = -12/5