Question

inverse Trig functions? sin^-1(cos5pi/6)

Answer 1

\[\sin^{-1} \left( \cos\frac{ 5\Pi }{ 6 } \right)\]

Answer 2

which quadrant is the angle 5pi/6 located in?

Answer 3

2

Answer 4

yes

Answer 5

what is cos(5pi/6) equal to?

Answer 6

\[-\frac{ \sqrt{3} }{ 2 }\]

Answer 7

yes

Answer 8

so `arcsin(cos(5pi/6))` turns into `arcsin(-sqrt(3)/2)`

Answer 9

?

Answer 10

arcsin is the same as \(\Large \sin^{-1}\)

Answer 11

yes. but why would it turn to arc sin instead of just cos?

Answer 12

\[\Large \sin^{-1}\left(\color{red}{\cos\left(\frac{5\pi}{6}\right)}\right) = \sin^{-1}\left(\color{red}{-\frac{\sqrt{3}}{2}}\right)\]

\[\Large \arcsin\left(\color{red}{\cos\left(\frac{5\pi}{6}\right)}\right) = \arcsin\left(\color{red}{-\frac{\sqrt{3}}{2}}\right)\]

Answer 13

oh ok

Answer 14

now use the unit circle

http://etc.usf.edu/clipart/43200/43215/unit-circle7_43215_lg.gif

Answer 15

which point in Q4 has a y coordinate of -sqrt(3)/2 ?

Answer 16

\[\frac{ 5\Pi }{ 3} ?\]

Answer 17

yep, so the final answer is 5pi/3

Answer 18

what about the 3rd quadrant. 4pi/3 also has -sqrt(3)/2

Answer 19

sorry I'm not thinking, the range of arcsine is -pi/2 <= y <= pi/2

so if we restrict ourselves to that interval, then the answer should be -pi/3

see page 3 of this pdf

http://www.math.tamu.edu/~austin/section4_6.pdf

Answer 20

hmmm

Answer 21

the range of arcsine is -pi/2 to pi/2

Answer 22

so whatever the output of arcsine, it will lie in Q1 or Q4

Answer 23

yes i know that but does this go for every problem similar to the one i asked?

Answer 24

yes if the outer most function is an inverse trig function (see that pdf for more details about the range of arcsine and arccosine)

Answer 25

how is it negative though. the only time i usually put negative is when it would have negative cos

Answer 26

positive angles mean you go counterclockwise (after facing directly east)