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for sin, cos, tan, csc, sec, and cot functions, how do you find the angles?

Mathematics
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i know you type in the calculator inverse sin..etc but like how do you know which quadrants they are in
the inverse functions \[\sin^{-1} or \space \cos^{-1} or \tan^{-1} \] and so on
i know that

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Other answers:

but how do you know which quadrant
once you find that reference angle
Ah, ok i got it
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.
hmmm still sorta confused. can you give me an example mertsj?
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.
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ok so like if i have sin x = 1/2
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so if i have sin = 1/2 that means y= 1 and R = 2
so then it would be first quadrant and third quadrant ?
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)
sorry x belongs to [0,360]
uhhhh..
for sin3x = 1/2 why is the answer pi/18 and 5pi/18 ?
\[3x= \frac{\pi}{6}, \frac{5\pi}{6}\] \[x=\frac{\pi}{18}, \frac{5\pi}{18}\]
but why
3x=1/6 What is x?
idk
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lol 1/18
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This is how I remember it: All Students Take Calculus It helps you remember which functions are positive. Quadrant 1 : They are all positive

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