Given sin x=-1/8 and tan x < 0, find sin 2x (without using a calculator).
Let's look at the allowed values for sin(x)....this is a sinusoidal function oscillating between -1 and 1 as does the cos(x) function
If you plot cos x and sin x, you will see something interesting which I will illustrate in the attached ...
Sin 2x is found without using a calculator. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.