## anonymous one year ago FAN AND MEDAL The point (1, −1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.

1. jdoe0001

$$\begin{array}{cccllll} (1&,&-1)\\ x&,&y \end{array}\qquad hypotenuse=r=\sqrt{x^2+y^2}\impliedby \textit{pythagorean theorem} \\ \quad \\ \quad \\ sin(\theta)=\cfrac{y}{r} \qquad % cosine cos(\theta)=\cfrac{x}{r} \qquad % tangent tan(\theta)=\cfrac{y}{x}\impliedby \textit{find "r", and plug and chug}$$

2. anonymous

Mg I know you from my school :/

3. anonymous

@carsonce I'm kinda homeschooled so...

4. DanJS

Draw the thing first

5. DanJS

'standard' - relative to the +x axis i believe

6. DanJS

|dw:1443138414973:dw|

7. DanJS

8. DanJS

You see how the components of that line are at right angles to the x and y axis?

9. DanJS

|dw:1443138594122:dw|

10. anonymous

yeah

11. DanJS

you have right triangles with side lengths of 1

12. DanJS

|dw:1443138683435:dw|

13. DanJS

you have the side lengths of the right triangle, apply the definition of sin cos and tan to that angle theta, and remember you are in the 4th quadrant

14. DanJS

Example $\sin(\theta) = \frac{ 1 }{ \sqrt{2} }$ $\theta =\sin^{-1} [\frac{ 1 }{ \sqrt{2} }] = 45$

15. DanJS

So the angle theta is 45, but recall you are in the 4th quadrant

16. anonymous

oooooh okay I see now

17. DanJS

So the theta is actually from +x CounterClockWise to that terminal side`

18. DanJS

360-45 = 315

19. anonymous

Thank you for your assistance. I'm usually pretty good at math, but trig is tripping me up so much...

20. DanJS

The sin value of theta and (360-theta) are the same, (the y value on the unit circle point)

21. DanJS

Right, me too when i took it, realize that the sin function is just the y-coord of the intersection of a line at angle theta through the origin and the unit circle of radius 1

22. DanJS

each point ON the unit circle of radius 1 centered at the origin, is (x , y) = ( cos(angle), sin(angle) )

23. DanJS

i fyou are that far yet

24. anonymous

Ah okay

25. DanJS

These may help, solved probs and stuff https://drive.google.com/folderview?id=0B1YZD9uzvB5TfnkzNzg5LU54VC1zUENBNHZoWlUxYXk1OXQtNklXdVVtZnA1T3c4X3hMMWM&usp=drive_web#list

26. DanJS

the last 5 of them

27. DanJS

oh forgot, here is a cheat sheet thing,

28. DanJS

gl