## HorribleAtMath for sin, cos, tan, csc, sec, and cot functions, how do you find the angles? 2 years ago 2 years ago

1. HorribleAtMath

i know you type in the calculator inverse sin..etc but like how do you know which quadrants they are in

2. y2o2

the inverse functions $\sin^{-1} or \space \cos^{-1} or \tan^{-1}$ and so on

3. HorribleAtMath

i know that

4. HorribleAtMath

but how do you know which quadrant

5. HorribleAtMath

once you find that reference angle

6. y2o2

Ah, ok i got it

7. Mertsj

Just remember that the cos is like x and the sin is like y. That gives you the sign of all the functions in all the quadrants.

8. HorribleAtMath

hmmm still sorta confused. can you give me an example mertsj?

9. y2o2

you have to check the value of the function in the first quad. all functions are positive in the second quad. sine is the only positive the rest are negative in the third quad. tan is the only positive the rest are negative in the fourth quad. cosine is the only positive the rest are negative so when you find the angle , you can determine in which quad it is.

10. y2o2

|dw:1332718026574:dw|

11. HorribleAtMath

ok so like if i have sin x = 1/2

12. Mertsj

|dw:1332717956955:dw|

13. HorribleAtMath

so if i have sin = 1/2 that means y= 1 and R = 2

14. HorribleAtMath

15. y2o2

for example if sin(x) = 0.5 and x belongs to [0,180] then x must be in the first or the second quad. because it's +ve and sin^-1(0.5) = 30 so x =30 or x = (180-30 = 150)

16. y2o2

sorry x belongs to [0,360]

17. HorribleAtMath

uhhhh..

18. HorribleAtMath

for sin3x = 1/2 why is the answer pi/18 and 5pi/18 ?

19. Mertsj

$3x= \frac{\pi}{6}, \frac{5\pi}{6}$ $x=\frac{\pi}{18}, \frac{5\pi}{18}$

20. HorribleAtMath

but why

21. Mertsj

3x=1/6 What is x?

22. HorribleAtMath

idk

23. Mertsj

|dw:1332719500565:dw|

24. Mertsj

|dw:1332719528422:dw|

25. HorribleAtMath

lol 1/18

26. Mertsj

|dw:1332719572812:dw|

27. precal

|dw:1332723649132:dw|

28. precal

This is how I remember it: All Students Take Calculus It helps you remember which functions are positive. Quadrant 1 : They are all positive