# Thread: [SOLVED] Inverse Trigonometric Functions

1. ## [SOLVED] Inverse Trigonometric Functions

Question:
How to do the inverse trigonometric function to find the exact value of:-
$\arcsin\frac{1}{2}$

Attempt:
I can do it using a calculator, but I don't know how to find it in the sine function graph ( I know how to draw the graph but I don't know what to do next)

Thank you

2. Originally Posted by mj.alawami
Question:
How to do the inverse trigonometric function to find the exact value of:-
$\arcsin\frac{1}{2}$
By definition, $\sin^{-1}\left(\frac{1}{2}\right)\, =\, \theta$ means that $\sin\left(\theta\right)\, =\, \frac{1}{2}$. For which value of $\theta$ is the value of sine equal to one-half?

3. To find the solutions on the sine graph, draw a straight line at x = (1/2). The intersections will be your solutions.

.

Hope that this helps,
mintsmike

4. Originally Posted by stapel
By definition, $\sin^{-1}\left(\frac{1}{2}\right)\, =\, \theta$ means that $\sin\left(\theta\right)\, =\, \frac{1}{2}$. For which value of $\theta$ is the value of sine equal to one-half?
I know the value but can you please show me the graph and how did you get the value from the graph?

Thank you

5. Originally Posted by mj.alawami
I know the value but can you please show me the graph and how did you get the value from the graph?

Thank you

$sin^{-1} 0.5$ is 30, as you clearly know. If you are familiar with the graph of $y = sinx$, then you can draw this and the line that you draw from 0.5 on the x-axis will meet at 30 degrees on the y-axis.
The graph can be shown here:
http://www.quickmath.com/www02/image...t/example4.gif
On the graph, take 3 as the value of 180 and hence 1 as 60. You can see that if you drew a line from 0.5, it would meet halfway to 1 - which is 30!

I hope this helps you in what you're trying to do!