SOLUTION: Find sin^-1 x for the given x. Express your answer as a rational multiple of pi. ranging from pi/2 to 3pi/2. sin^-1 0.5=? how do you solving these kind of problems???

Question 964616: Find sin^-1 x for the given x. Express your answer as a rational multiple of pi. ranging from pi/2 to 3pi/2. sin^-1 0.5=? how do you solving these kind of problems???
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
sin^-1 0.5 = ?
This problem is asking you to calculate the inverse sign function for 0.5, the answer can be in degrees or radians. If your teacher allows you to use a calculator, then look for the sin^-1 function. Sometimes the calculator will have an inverse function that applies to trig functions.
***********************************************************
sin^-1 0.5 = 30 degrees, which implies that sin 30 = 0.5
note that 30 degrees is not the only answer, since trig functions have a period of 360 degrees.
***********************************************************
We are asked to evaluate sin^-1 0.5 over pi/2 to 3pi/2. Note that pi is 180 degrees for trig functions, therefore
we evaluate sin^-1 0.5 from 90 degrees to 270 degrees
***********************************************************
sin 150 = 0.5,
note sin 210 = -0.5
therefore between 90 degrees and 270 degrees, we have one answer sin 150 = 0.5
now we need to convert 150 to a rational multiple of pi (180)
150 / 180 = 5pi / 6
**************************************************************
consider the graph of the sin function

The minimum of the first dip below the x-axis corresponds to 270 degrees and the first maximum above the x-axis corresponds to 90 degrees. Now the values on the y-axis range over +1 to -1, so if you draw a line (green line) parallel to the x-axis half way between 0 and 1 (0.5), you see that there is just one positive value between 90 and 270 degrees.

RELATED QUESTIONS
Find tan ^-1 x for the given x. Express your answer as a rational multiple of pi, ranging (answered by Alan3354)

Inverse sin of 1/sqrt root 2 or (sin^-1(1/sqrt root 2). Find sin ^-1 x for the given x.... (answered by josgarithmetic)

Can someone please explain to me why pi/4 is not the correct answer for this question? (answered by josgarithmetic)

Express your answer as a rational multiple of pi ranging from pi/2 to 3pi/2... (answered by stanbon)

Solve the equation for 0≤x≤{{{2pi}}}. Write your answer as a multiple of... (answered by Gogonati,Alan3354)

Solve the equation for 0≤x≤2pi. Write your answer as a multiple of pi if... (answered by Edwin McCravy)

This is a multiple angles question: sin x/2 = sqrt(2)/2 For the answer, I got pi/2... (answered by Alan3354)

This is a question on a practice test that I don't know how to solve or get the answer... (answered by htmentor)

Sin x = 1/3 ,0 < x < pi/2 Cos y = 2/5 ,0 < x < pi/2 Find sin (x+y) (answered by ikleyn)