If csc theta = 2, then what is theta approximated to 4 decimal points?
RADIANS
if cscØ = 2, then sinØ = 1/2
Ø = 30° or π/6 radians or appr .5236 rad
To find the approximate value of theta when csc(theta) is equal to 2, we need to use the inverse cosecant function, also known as the arcsin function.
The inverse cosecant function, denoted as csc^(-1)(x) or arcsin(x), gives the angle whose cosecant is equal to x.
In this case, csc(theta) is equal to 2. So, we can write it as:
csc(theta) = 2
To find the value of theta, we can take the inverse cosecant of 2:
theta = csc^(-1)(2)
Now, let's calculate this using a calculator:
1. Turn on your calculator and make sure it is set to radians mode.
2. Enter the value 2.
3. Press the inverse cosecant button (usually labeled as "csc^(-1)" or "arcsin").
If your calculator does not have an inverse cosecant button, you can use the reciprocal identity of cosecant:
csc^(-1)(x) = sin^(-1)(1/x)
In this case, we have:
theta = sin^(-1)(1/2)
So, you need to find the inverse sine of 1/2.
Here's how you can calculate it:
1. Turn on your calculator and set it to radians mode.
2. Enter the value 1/2.
3. Press the inverse sine button (usually labeled as "sin^(-1)" or "arcsin").
After performing the calculation, you will get the value of theta. Round this value to 4 decimal places to approximate theta.