Can anybody help me with this following question, I never heard of it before...until now:
If tan θ = x where θ is acute, find in the terms of x:
a) 2 sin θ.
b) 3 cos θ.
What does θ acute in this case represent?
In terms of x...
if $\displaystyle tan\theta=x$
$\displaystyle tan\theta=\frac{x}{1}=\frac{opposite}{adjacent}$ in a right-angled triangle.
Using Pythagoras' theorem
$\displaystyle hypotenuse=\sqrt{adj^2+opp^2}=\sqrt{1+x^2}$
$\displaystyle 2sin\theta=2\frac{opp}{hyp}=\frac{2x}{\sqrt{1+x^2} }$
$\displaystyle 3cos\theta=3\frac{adj}{hyp}=\frac{3}{\sqrt{1+x^2}}$