CSC(theta)=1.92
Find Theta.
Now I know CSC = 1/sin but no matter how I enter it into my cal I get an error.
1.92 = 192 / 100 = 3 * 64 / 100 = 3 * 2 ^ 6 / 2 ^ 2 * 25
1.92 = 3 * 2 ^ 4 / 25
csc ( theta ) = 3 * 16 / 25
csc ( theta ) = 48 / 25
theta = arc csc ( 48 / 25 ) = arc sin ( 25 / 48 )
theta = 31° 23´ 17½
Don't know why "anonymous" went through all that ...
just do:
cscØ = 1.92
sinØ = 1/1.92 = .52808333... (keep that number in your calculator)
Ø = sin^-1 (.5280833...) = appr 31.388°
if you need your angle in radians, switch your calculator to R with the DRG key and repeat the last step
Ø = .5478 radians
To find the value of theta when CSC(theta) = 1.92, we need to solve for theta using the inverse trigonometric function of CSC, which is arcsin.
However, it seems that you are encountering an error when entering the inverse trigonometric function into your calculator. This could be due to a couple of reasons:
1. Ensure that your calculator is set to the correct mode: Make sure your calculator is in degree or radian mode, depending on how the value of theta is expected to be expressed.
2. Use the appropriate notation: Different calculators have different notations for inverse trigonometric functions. Some use "arcsin," while others use "sin^(-1)" or "asin." Refer to your calculator's manual or guide to determine the correct notation.
Now, let's solve for theta using a scientific calculator:
1. Enter 1/1.92 (since CSC(theta) = 1/sin(theta) = 1.92).
2. Then, find the inverse sine of the resulting value, using the appropriate notation for your calculator ("arcsin," "sin^(-1)," or "asin").
3. Press the appropriate button to calculate the inverse sine.
4. The resulting value should be the value of theta.
Ensure that you follow the correct order of operations and that any parentheses are appropriately placed when entering the expression into your calculator.
If you are still unable to obtain the result, it is recommended to consult your calculator's manual or guide for further assistance with solving inverse trigonometric functions.