Question

If cos A=4/5 and A is in quadrant I what is the value of sin A * tan A

Answer 1

Step-by-step explanation:

Let's call the quadrant 1 angle, "A".

Let a right triangle be constructed in quadrant 1 such that angle A is the angle between the hypotenuse of length 5 and the adjacent side or base of the triangle that is of length b.

Sine A = 4/5 = (Length of the side opposite angle A, a)/(Length of the hypotenuse) = OPP. SIDE/HYP.

Cosine A = (Length of adjacent side to angle A, b)/(Length of the hypotenuse) = ADJ. SIDE/HYP.

Using the Pythagorean Theorem, a^2 + b^2 = c^2, where, in this problem, the length of the hypotenuse is c = 5, we can calculate and find that we actually have a 3-4-5 right triangle since the length of the side adjacent to angle A, b, equals 3; therefore, ...Cosine A = ADJ. SIDE/HYP. = b/c = 3/5.