Consider △DFE. What are the inputs or outputs of the following trigonometric ratios? Express the ratios in simplest terms.
Accepted Solution
A:
Answer: sin F = 4/5 cos F = 3/5 tan D = 3/4
Explanation: First, we have sin an angle = 4/5 In a right-angled triangle: sin theta = opposite / hypotenuse This means that in triangle DFE: The hypotenuse = 5 units one of the sides = 4 units Use Pythagorean theorem to get the other side as follows: hypotenuse^2 = side1^2 + side2^ 25^2 = 4^2 + side2^2 side2^2 = 9 The second side of the triangle = 3 units
The special trig functions are as follows: sin theta = opposite / hypotenuse cos theta = adjacent / hypotenuse tan theta = opposite / adjacent From the attached figure and based on the calculations above: sin F = 4/5 cos F = 3/5 tan D = 3/4 Hope this helps :)