## cutiecomittee123 one year ago If sintheta=2/3 which of the following are possible? sectheta= -3/2 and tantheta= 2/root5 costheta= -root5/3 and tantheta= 2/root5 costheta= root5/3 and tantheta= 2/root5 sectheta= 3/root5 and tantheta= 2/root5

1. anonymous

|dw:1443065980821:dw|

2. anonymous

First find the missing side. We know that sin$$\theta$$=$$\frac{2}{3}$$, so the opposite side is $$2$$, and the hypotenuse is $$3$$. Now we need to find the adjacent. Use the Pythagorean theorem. $$c^2=a^2+b^2$$ $$3^2=2^2+b^2$$ $$b^2=9-4$$ $$b=\sqrt{5}$$ So the adjacent side is $$\sqrt{5}$$.

3. cutiecomittee123

okay im with it so far

4. anonymous

So now we know the three sides: opposite: 2 adjacent: $$\sqrt {5}$$ hypotenuse: 3 ---- We know that $$\huge cos\theta$$=$$\huge \frac {adjacent}{hypotenuse}$$ so $$\huge cos\theta$$=$$\huge \frac {\sqrt{5} }{3}$$

5. cutiecomittee123

Now that we have the sides which are 2,3, and -root5 we know that sin=-3/root5 cos=2/5 tan=3/2 sec=-root5/2 csc= -root5/3 and cot= 2/3

6. cutiecomittee123

i didnt mean negative root 5 just root 5

7. cutiecomittee123

but i also see that i messed up

8. cutiecomittee123

Oops okay i had them in the wrong order then

9. anonymous

And $$\tan\theta =\huge \frac {oposite}{adjacent}$$, so $$\tan\theta =\huge \frac {2}{\sqrt{5}}$$ or $$\huge \frac {2\sqrt{5}} {5}$$ .

10. anonymous

opposite*

11. cutiecomittee123

So that means that the last two in my question are the best two options

12. anonymous

Yes! :)