Given Cot x = -5, sin x = sqrt(36)/26, evaluate 6 trig fcns

NoAsherelol

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Given Cot x= -5 and sin x= (Sqaure root of 26)/26 evaluate all six trig functions

Im only in 10th grade why is this stuff so hard, i though trig functions are inbetween the intervals -1<0<1
 
Not all the trig functions are between -1 and 1 exclusively. csc, sec, cot have values > 1

Anyway, I posted a diagram to help get you started. See, by Pythagoras, we find that the hypoteneuse is

r=(5)2+12=26\displaystyle r=\sqrt{(-5)^{2}+1^{2}}=\sqrt{26}

Now, from that you can derive all the other ones.

We have x=5,   y=1,   r=26\displaystyle x=-5, \;\ y=1, \;\ r=\sqrt{26}

You have sin(x), which is yr=126=2626\displaystyle \frac{y}{r}=\frac{1}{\sqrt{26}}=\frac{\sqrt{26}}{26}

xr=cos(x)\displaystyle \frac{x}{r}=cos(x)

yx=tan(x)\displaystyle \frac{y}{x}=tan(x)

rx=sec(x)\displaystyle \frac{r}{x}=sec(x)

ry=csc(x)\displaystyle \frac{r}{y}=csc(x)

There, I am sure you can finish now. Okey-doke?.
 

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sin(x)=2626=126&cot(x)=55=cos(x)sin(x)=26cos(x)\displaystyle \begin{array}{l} \sin (x) = \frac{{\sqrt {26} }}{{26}} = \frac{1}{{\sqrt {26} }}\,\& \,\cot (x) = - 5 \\ - 5 = \frac{{\cos (x)}}{{\sin (x)}} = \sqrt {26} \cos (x) \\ \end{array}
 
yes i figured it out thanx for the help guys, i really appreciate it, i thought trig was fun lol, wish i was back in my 3rd grade days lol
 
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