## AmTran_Bus 3 years ago Find exact answer...easy trig

1. AmTran_Bus

|dw:1351550575736:dw|

2. AmTran_Bus

If theta equals tan theta and that equals 3, find F(theta+pi)

3. AmTran_Bus

@freewilly922 @swissgirl

4. AmTran_Bus

|dw:1351550836023:dw|

5. anonymous

not sure hoe theta can equal tan theta

6. anonymous

unless theta equals 0

7. anonymous

But cant see it when theta equals 3

8. AmTran_Bus

Well, I think you can also read it as tan theta=3, and it wants you to find the exact value using the coord plane.

9. AmTran_Bus

And something about when you add pi you go 180 degrees around the unit circle...

10. anonymous

1) you know that the tangent is positive so if you start in quadrant 1 you know that the triangle that you draw the opposite side to the angle has to be 3 times that of the adjacent side. |dw:1351551020275:dw| adding pi or 180 degrees puts you in the 3rd quadrant where both sin and cos are both negative, so the negatives signs will cancel out. Therefore, tan(theta) = tan(theta+180) = 3

11. anonymous

Oh and pi(radians) = 180 degrees and yes I know it should be a 3 in the drawing

12. AmTran_Bus

Tan= y/x ...do you use the value of x or y in this example?

13. anonymous

|dw:1351551191480:dw| $\tan{(\theta)} = \frac{\sin{(\theta})}{\cos{(\theta)}}$ when you go to the 3rd quadrant you go from a y/x to a (-y)/(-x) so you stay with y/x

14. anonymous

$\frac{\sin{(\theta)}}{\cos{(\theta)}}=\frac{y}{r}\frac{r}{x}$