## AmTran_Bus Group Title Find exact answer...easy trig one year ago one year ago

1. AmTran_Bus Group Title

|dw:1351550575736:dw|

2. AmTran_Bus Group Title

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

3. AmTran_Bus Group Title

@freewilly922 @swissgirl

4. AmTran_Bus Group Title

|dw:1351550836023:dw|

5. swissgirl Group Title

not sure hoe theta can equal tan theta

6. swissgirl Group Title

unless theta equals 0

7. swissgirl Group Title

But cant see it when theta equals 3

8. AmTran_Bus Group Title

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 Group Title

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

10. freewilly922 Group Title

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. freewilly922 Group Title

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

12. AmTran_Bus Group Title

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

13. freewilly922 Group Title

|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. freewilly922 Group Title

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