Final answer:
To express the trig ratios as fractions in simplest terms, use the Pythagorean identity to find the opposite side of the triangle for cosQ and sinP. Both cosQ and sinP are equal to 4/5.
Step-by-step explanation:
To express the trig ratios as fractions in simplest terms, we need to use the Pythagorean identity. Let's start with the cosine ratio cosQ = \(\frac{4}{5}\). Since cosQ represents the ratio of the adjacent side to the hypotenuse, we can let the adjacent side be 4 and the hypotenuse be 5. Using the Pythagorean theorem, we can find the opposite side of the triangle:
\(\sqrt{5^2 - 4^2} = \sqrt{25 - 16} = \sqrt{9} = 3\)
So, sinQ = \(\frac{3}{5}\).
Similarly, let's find sinP by using the given cosQ = \(\frac{4}{5}\). Since cosQ represents the ratio of the adjacent side to the hypotenuse, we can let the adjacent side be 4 and the hypotenuse be 5. Using the Pythagorean theorem, we can find the opposite side of the triangle:
\(\sqrt{5^2 - 4^2} = \sqrt{25 - 16} = \sqrt{9} = 3\)
So, sinP = \(\frac{3}{5}\).
Therefore, both cosQ and sinP are equal to \(\frac{4}{5}\).