Question

How would you solve/approach this:
sin−1(sin(7π/3))

Answer 1

Sin-1(sin x) =x

Answer 2

yes true!

Answer 3

now i have
sin−1(sin(7π/3)=7π/3
do i divide each side by sinx?

Answer 4

remember though we want x to be between -pi/2 and pi/2

Answer 5

recall sin(pi/3)=sin(7pi/3)
so
sin^{-1}(sin(7pi/3))=sin^{-1}(sin(pi/3))=pi/3

Answer 6

oh it is sin-1(sin(7pi/3))?

Answer 7

how do you know pi/3 = 7pi/3?

Answer 8

this doesn't make any sense then

Answer 9

sin(pi/3)=sin(7pi/3)

Answer 10

i didn't say pi/3=7pi/3

Answer 11

your job is to find the number between
\[-\frac{\pi}{2},\frac{\pi}{2}\] whose sine is given. in other words look on the right side of the unit circle, and find an agle coterminal with
\[\frac{7\pi}{3}\]

Answer 12

*angle

Answer 13

right since the range of sine inverse is (-pi/2,pi/2)

Answer 14

to be pedantic is it
\[[-\frac{\pi}{2}, \frac{\pi}{2}]\]

Answer 15

is pi/6 coterminal to 7pi/3?

Answer 16

lol very good satellite

Answer 17

what is 7pi/3-2pi?

Answer 18

no because your denominator is wrong. should be
\[\frac{7\pi}{3}-2\pi=\frac{\pi}{3}\]

Answer 19

oh sorry

Answer 20

oh! i see

Answer 21

math really isn't my subject :/
but so once i have sin-1(sin(pi/3))
then since that equals x, does it evaluate to pi/3?

Answer 22

you could also do this problem the donkey way, but just saying
\[\sin(\frac{7\pi}{3})=\frac{\sqrt{3}}{2}\] and then finding
\[\sin^{-1}(\frac{\sqrt{3}}{2})\]which is
\[\frac{\pi}{3}\] but that is the silly way

Answer 23

yes, answer is
\[\frac{\pi}{3}\]

Answer 24

why is that the silly way just wondering? lol

Answer 25

what I don't understand is how you find what sin(7pi/3) equals?

Answer 26

how do i know it?

Answer 27

like how do you solve that?

Answer 28

i find
\[\frac{7\pi}{3}\] on the unit circle and look at the second coordinate
that is the sine
first coordinate is cosine

Answer 29

look at the unit circle on last page of cheat sheet. find the angle you are looking for and then look at the second coordinate

Answer 30

isn't that -1/2

Answer 31

first coordinate is 1/2

Answer 32

because isn't the coordinate is (-sqrt3/2, -1/2)?

Answer 33

by counting out around the circle you will see that
\[\frac{7\pi}{3}\] is coterminal with
\[\frac{\pi}{3}\]

Answer 34

this is what confuses me. 7pi/3 isn't on the unit circle.