Find sin (tan^-1 1/3) in exact form and write 91°56'32" in decimal degrees.
Use a right triangle with legs 1 and 3 to calculate the trigonometric ratios.
Determine the length of the hypothenuse using the Pythagorean theorem:
Substitute 1 for `L_1` and 3 for `L_2`
In the figure below:
Therefore sin A = `1/sqrt10`
Divide minutes by 60 to convert them to decimals and divide seconds by 3600 to comvert them to decimals. Add them together to obtain the decimal part.
` `Use a common denominator to add them.
Therefore 91 degrees 56 minutes and 32 seconds is equal to 91.9422 degrees.