# Thread: Some more Trig questions

1. ## Some more Trig questions

Need some help on these problems. Help would be much appreciated:

1) find sin x/2, cos x/2, and tan x/2 from the given information:

cot x = 5, 180 degrees < x < 270 degrees

2) write the product as a sum

11 sin x/2 cos x/4

3) Find sin 2x, cos 2x and tan 2x from the given information

sec x = 2, x in quadrant IV

Thanks in Advance

2. Alright, let me help you:
1) $cot(x)=\frac{1}{tan(x)}=5 <=>1=5*tan(x) <=>\frac{1}{5}=tan(x) <=>arctan(\frac{1}{5})=x$

Take out your calculator, and you will find x=11°18'35.8"
Now 180° < x < 270° , thus the III quadrant, so we add 180° to 11°18'35.8" : giving us 191° 18' 35.8"

I guess you can calculate the rest yourself.

2) This is typical Simpson Formula problem: thus i refer to List of trigonometric identities - Wikipedia, the free encyclopedia

3)This is more or less tricky. You'd best transform sec(x) into an cos(x)-function:

$\frac{1}{cos(x)}=sec(x)$

since x belongs to the IV quadrant, the $cos(x)$ is equal to $cos(x)$ for x belonging to the I quadrant. Now we do the same as in 1):

$\frac{1}{cos(x)}=2 <=>\frac{1}{2}=cos(x) <=> 45°=x$

You can calculate the rest now i guess: $sin(2*45°)=sin(90°)=1$ and etcetera

I hope this solves your problem. One advice for trigonometric problems: learn your table of common sin, cos and tan values at common angles, such as: 30°, 60°, 90°. Have trigonometric fun!