trigonometry
posted by Yulieth on .
if cosθ=2/3 and tanθ<0 find the exact value
sin(θ5π/3)
sin2θ
cos2θ
cos(θ/2)
can some1 please help me?

Solution:Step1First replace x with (xÎ”x) in the given funicton f(x) to obtainf(x+Î”x) = 2(x+Î”x)+1 = 2x + 2Î”x + 1 Step2Rewrite f(xÎ”x) as (2x + 2Î”x + 1) and f(x) as (2x + 1) into the definition of the derivative limit to obtain: lim [(2x + 2Î”x + 1)  (2x+1)] / Î”xÎ”x> 0 Step 3Combine like terms on the numerator and the reduced expression becomes lim [2Î”x] / Î”xÎ”x> 0 Step 4Cancel out Î”x from both numerator and denominator and finally you get the derivative Derivative of f (x) = 2x+1 = 2 Note there was no need to substitute Î”x with 0 since it was canceled out.