Question

Complete the statement. In your answer, rationalize the denominator and write it in simplest form.

If tan(x) = 3/5, and x is an angle in quadrant I, what is the value of cos(x)

Answer 1

To find the value of cos(x), we use the given information that tan(x) = 3/5 and x is in quadrant I. By assuming values for the opposite and adjacent sides of the right triangle, we can use the Pythagorean theorem to find the hypotenuse. Finally, we can use the values of the opposite and hypotenuse sides to find the value of sine, and the value of the adjacent and hypotenuse sides to find the value of cosine.

Step-by-step explanation:

To find the value of cos(x), we need to use the given information that tan(x) = 3/5 and x is an angle in quadrant I.

Since tan(x) = opposite/adjacent, we can find the values of the opposite and adjacent sides of the right triangle. Let's assume the opposite side is 3 and the adjacent side is 5.

Using the Pythagorean theorem, we can find the hypotenuse:

hypotenuse^2 = opposite^2 + adjacent^2

hypotenuse^2 = 3^2 + 5^2

hypotenuse = √(9 + 25) = √34

Now we can use the values of the opposite and hypotenuse sides to find the value of sine, and the value of adjacent and hypotenuse sides to find the value of cosine:

sin(x) = opposite/hypotenuse = 3/√34 = (3√34)/34

cos(x) = adjacent/hypotenuse = 5/√34 = (5√34)/34