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

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flbyrne | (Level 3) Assistant Educator

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Use a right triangle with legs 1 and 3 to calculate the trigonometric ratios.

Determine the length of the hypothenuse using the Pythagorean theorem:

hypothenuse`=sqrt(L_1^2+L_2^2)`

Substitute 1 for `L_1` and 3 for `L_2`

hypothenuse=`sqrt(1^2+3^2)=sqrt10`

In the figure below:

`tanA=1/3`

`A=tan^-1(1/3)`

`sinA=1/sqrt(10)`

Therefore sin A = `1/sqrt10`

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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.

`56/60+32/3600`

` `Use a common denominator to add them.

`(3360+32)/3600=0.9422`

Therefore 91 degrees 56 minutes and 32 seconds is equal to 91.9422 degrees.

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