Find sin (tan^-1 1/3) in exact form and write 91°56'32" in decimal degrees.

Expert Answers
flbyrne eNotes educator| Certified Educator

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.

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