Question

how do i do cos 5pi/4? or costheta=1/2
how do i differentiate y=sin (2x+pi/4) when x=0 to find the tangent and the normal?
also, how do i find the equation of the normal to y=ln(x+2) which is parallel to the line with the equation, y+3x-5=0, i know it has to have the same gradient which is -3 but i don't know how to go from there.

Answer 1

this is a 3rd quadrant angle where cos is negative so fine

\[\cos ( \frac{5\pi}{4} = - \cos (\frac{\pi}{4})\]

next is

\[\cos(\theta) = \frac{1}{2}....then...... \theta = \cos^{-1}(\frac{1}{2})\]

find the arc cos... and from the exact value triangle