1. ## [SOLVED] Trigonometry help!

Find the exact value of the other five trigonometric functions of theta:
(a) sin theta=5/13,and cos theta>0
(b)cos theta=-4/5,and sin theta >0
(c)tan theta=15/8,and sec<0
(d)cot theta=-5/12,and csc theta<0
(e)csc theta=-2,and cot theta>0

How to do this questions because i don't understand what i am supposed to do ....

2. Originally Posted by mj.alawami
Find the exact value of the other five trigonometric functions of theta:
(a) sin theta=5/13,and cos theta>0
(b)cos theta=-4/5,and sin theta >0
(c)tan theta=15/8,and sec<0
(d)cot theta=-5/12,and csc theta<0
(e)csc theta=-2,and cot theta>0

How to do this questions because i don't understand what i am supposed to do ....
Hello mj,

(a) $\sin \theta=\frac{5}{13} \ \ \cos \theta>0$

Sine and cosine are both positive in the 1st quadrant, only.

$r^2=x^2+y^2$

$\sin=\frac{y}{r}$.... $\cos=\frac{x}{r}$.... $\tan=\frac{y}{x}$

$\csc=\frac{r}{y}$.... $\sec=\frac{r}{x}$.... $\cot=\frac{x}{y}$

From (a), we get y = 5 and r = 13. So $13^2=x^2+5^2$
and eventually get $x=12$

Now that we know x = 12, y = 5, r = 13, we can find the other ratios above by substituting these values.