Explanation: csc θ = 1 / sin θ In a right angled triangle, sin θ = opposite / hypotenuse This means that: csc θ = hypotenuse / opposite = 8 / 7 So, we have: opposite = 7 units and hypotenuse = 8 units We will use the Pythagorean theorem to get the adjacent side as follows: (hypotenuse)^2 = (opposite)^2 + (adjacent)^2 (8)^2 = (7)^2 + (adjacent)^2 (adjacent)^2 = 15 adjacent = √15 units
Now, we want to get the value of cot θ. We know that: cot θ = 1 / tan θ Since tan θ = opposite / adjacent Therefore: cot θ = adjacent / opposite = √15 / 7
For this case you must take into account the following: 1) Trigonometric properties. 2) trigonometric equations 3) Division of fractions. Answer: cotx = root (15) / 7 See attached image.
