Question

Evaluate each trig value. List the ordered pairs. Simplify all fractions and rationalize all denominators.

a. sin(theta) = 3/5, cos(theta) = 4/5, tan(theta) = 3/4
b. sin(theta) = 1/2, cos(theta) = √3/2, tan(theta) = √3
c. sin(theta) = 2/3, cos(theta) = 3/5, tan(theta) = 2/3
d. sin(theta) = 5/13, cos(theta) = 12/13, tan(theta) = 5/12

Answer 1

Trigonometric values provided for each angle theta result in the ordered pairs (3/5, 4/5, 3/4), (1/2, √3/2, √3), (2/3, 3/5, 2/3), and (5/13, 12/13, 5/12) respectively. Simplification is not needed as they are already given in simplest form.

Step-by-step explanation:

Evaluating each trigonometric value and listing the ordered pairs simply requires using the given sine, cosine, and tangent values to construct the pairs. Simplification of fractions and rationalization of denominators may be necessary when the values are not already in simplest form.

• (sin(θ), cos(θ), tan(θ)) for each set of trigonometric values:
• a. (3/5, 4/5, 3/4)
• b. (1/2, √3/2, √3)
• c. (2/3, 3/5, 2/3)
• d. (5/13, 12/13, 5/12)

Each of these ordered pairs represents the sine, cosine, and tangent values for a particular angle θ. These values suggest that the trigonometric functions already satisfy the Pythagorean identity: sin2(θ) + cos2(θ) = 1, indicating that they are likely derived from a right triangle or are part of a unit circle. The tangent value, being the ratio of sine to cosine, also appears to have already been simplified.