If cot θ = 5/12, what is the value of sin θ?

If cot θ = 5/12, what is the value of sin θ?

Step 1: Understand that cot θ = 5/12 means that the adjacent side is 5 and the opposite side is 12 in a right triangle.
Step 2: Use the Pythagorean theorem to find the hypotenuse. The formula is hypotenuse^2 = adjacent^2 + opposite^2.
Step 3: Calculate the hypotenuse: hypotenuse^2 = 5^2 + 12^2 = 25 + 144 = 169.
Step 4: Find the hypotenuse by taking the square root: hypotenuse = √169 = 13.
Step 5: Now, use the definition of sine: sin θ = opposite / hypotenuse.
Step 6: Substitute the values: sin θ = 12 / 13.

Trigonometric Identities – Understanding the relationship between cotangent, sine, and cosine, and how to manipulate these identities to find unknown values.
Pythagorean Theorem in Trigonometry – Applying the Pythagorean theorem to find the lengths of the sides of a right triangle when given one of the trigonometric ratios.