trigonometry
Given $\sin(A)=x$, and that $90^\circ<A<180^\circ$, find the value of $\tan(2A)$ in terms of $x$ and/or $y$.
From the question I understand that A is in the 2nd quadrant (since sin positive) and B is in the 4th quadrant (since cos positive). However from there I'm stuck. Thanks in advance 🙂
At Chandru's request:
The quadratic $12z^2-7z-12$ factors as $(3z-4)(4z+3)$ so we should get $\tan\,\theta=4/3$ and $\tan\,\theta=-3/4$.
"Acute angle" means "angle between 0 and $\pi/2$" means 1st quadrant.
This is a table that expresses sin, cos and tan in terms of each other.
You don't need to remember the table... just substitute values in the triangle, find the third side using Pythagoras and find the value of the required function.
Also, you just need to remember which trigonometric function is positive in which quadrant using this table.
This can be remembered using the simple mnemonic.. After School To College.
Best Answer
With your conditions $$\tan{A}=\frac{\sin{A}}{\cos{A}},$$ $$\cos{A}=-\sqrt{1-x^2}$$ and
$$\tan2A=\frac{2\tan{A}}{1-\tan^2A}$$ Can you end it now?