How do I find all angles 0°≤theta<360°, that satisfy the equation below, to the nearest tenth of a degree 4sin x cos x =5cos x?

Answer 1

Greetings! Lets solve this shall we ?

So, we must find all angles x that satisfy the given equation such that

4sinxcosx = 5cosx..................We subtract 5cosx from both sides to obtain

4sinxcosx - 5cosx = 0.............Then we factor cosx out to get

cosx(4sinx - 5) = 0.............Then we apply the Zero-Product Property of Equality to get

cosx = 0 and 4sinx - 5 = 0.........Then

x = cos^-1(0) = 90^o & 270^o Next,

4sinx - 5 = 0..........Add 5 to both sides to get

4sinx = 5.........Then divide 4 to obtain

sinx = 5/4............Then take the sine inverse to both sides to solve for x to get

x = sin^-1(5/4) = Does Not Exist because the domain of the inverse function is greater than 1.

I hope this helped!