Question

How would you find the General Solution to the Trigonometric function (Look in replies)

Answer 1

\[y=arcsin (\frac{- \sqrt3 }{ 2 })\]

Answer 2

Its _____Plus or Minus 2kPI

Answer 3

@hartnn

Answer 4

sin function take an angle and read back a ratio

arcsin reverses the process, it takes a ratio and gives back the angle

Answer 5

so, what arc (angle) has a sine of -sqrt3/2 ?

Answer 6

uhm. I honestly have no clue. How would I find it?

Answer 7

you either need to use a calculator that has inverse trig function on it, or if this is one of the special simpler triangle ratios then it would be useful to put those few triangles to memory

Answer 8

I have a calculator with Inverse trig functions on hand.

Answer 9

i recall that an equallateral triangle has the sides we need

but the calculator is just as well

Answer 10

Okay, so how would I input something like this into my calculator to give me the answer I am looking for?

Answer 11

depends on the calculator really.

a ti83 for instance, hit 2nd, sin, and input -sqrt3/2

others ive used would have you input -sqrt3/2 and then press the inverse sine key

Answer 12

one small issue with the calulator is that its gonna try to calculate the pi part of it into the answer and your not gonna have an 'exact' result;

Answer 13

the special triangle method, or a unit circle chart are really useful in this case

Answer 14

I have a unit circle on hand also.

Answer 15

use the unit circle and find the angle that has a sin value of -sqrt3/2 .... or |sin| = sqrt3/2

Answer 16

Would my answer be pi/3? Because the Square root of -3/2 is .866. the Arcsin of .866 is approx. 60.

Answer 17

almost.

pi/3 has a sine of sqrt3/2

-pi/3 has a sine of -sqrt3/2 :)

Answer 18

My options are

pi/3
2pi/3
4pi/3
5pi/3

Answer 19

well, then we have to work with 2pi instead of 0pi, since 2pi = 0pi in trig stuff

2pi - pi/3 = ?

Answer 20

aproxx. 5.23

Answer 21

technically, arcsin is a function that has a range from -pi/2 to pi/2 so -pi/3 is correct and the options are wrong

but other than that: 5pi/3 is the same point in the unit circle as -pi/3 so they are equivalent.

Answer 22

95% of trig stuff is memorization and mental gymnastics ....

Answer 23

Okay, I see that now. Since 5pi/3 is in quadrant IV, The Sin and Cosin are both negative. Okay okay. I finally understand! Thank you so Much!

Answer 24

I hate trig. Its a royal pain.

Answer 25

:) good luck

Answer 26

can you assist with one more? Its a quick one

Answer 27

maybe

Answer 28

Gotta find the Inverse of f(x)=2arcsinx

Answer 29

The inverse of an inverse :o So wouldnt it be 2sin(x)?

Answer 30

not quite

an inverse function has the property that if f(x) and g(x) are inverses: then f(g) = x

f(g(x)) = 2 arcsin(g(x))

arcsin undoes sin so we know there has to be a sin involved

2 arcsin(sin(u)) = 2u

when does 2u = x? solve for u

Answer 31

f-1(x)=sin(x/2)

Answer 32

correct

Answer 33

These are my options

1/2 sin(x)
sin(1/2x)
sin(2x)
2sin(x)

Answer 34

1/2 x is the same as x/2

Answer 35

Thanks man :) I appreciate it.

Answer 36

yw :)