Thread: Solving Trig problems

Okay so i have two problems that I cant solve completely.
One is a a word problem
1. A sharpshooter intends to hit a target at a distance of 1000 yards with a rifle having a muzzle velocity of vo=1200 feet per second. Neglecting air resistance, determine the gun's minimum angle of elevation x if the range r is given by
r=(1/32)vo^2(sin(2x))
I can solve this problem down to 1/15 = sin(2x) (assuming i did this much right).
My second problem is:
Solve tan(x+pi)+2sin(x+pi)=0 i started to solve this using the sum and difference formulas.
If anyone could help that would be great. Thanks
AC

Originally Posted by Casas4

Okay so i have two problems that I cant solve completely.

My second problem is:
Solve tan(x+pi)+2sin(x+pi)=0 i started to solve this using the sum and difference formulas.
If anyone could help that would be great. Thanks
AC

$\displaystyle \tan(x+\pi)+2\sin(x+\pi)=0$

$\displaystyle \implies \frac{\sin(x+\pi)}{\cos(x+\pi)}+2\sin(x+\pi)=0$

$\displaystyle \implies \sin(x+\pi)\bigg[\frac{1}{\cos(x+\pi)}+2\bigg]=0$

We can get 2 equations out of this:

$\displaystyle \sin(x+\pi)=0$ and $\displaystyle \cos(x+\pi)=-\tfrac{1}{2}$

Can you take it from here? You don't need to apply the sum and difference formulas here.

--Chris

I can solve this problem down to 1/15 = sin(2x) (assuming i did this much right).

The next step is, depending on the notation you use,
$\displaystyle 2x = \arcsin(\frac{1}{15})$
or
$\displaystyle 2x = \sin^{-1}(\frac{1}{15})$
You then solve for x normally by dividing both sides by 2.

What the notation actually means is inverse sin, so if y = sin(x) then x = arcsin(y).

Often you will be expected to answer in turns of arcsin, but if you have a calculator you can turn it into a decimal approximation. the button on the calculator will probably be labelled $\displaystyle \sin^{-1}$ or asin.