Evaluating Inverse of Trig Functions

BlueStreak

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May 29, 2019
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Evaluate: sin(tan-1 5/12)

I don't know how to do this without a calculator. Please help.
 
Evaluate: sin(tan-1 5/12) ...
Hello. Start by remembering what the arctangent and sine functions each input and output.

A trig ratio goes into arctangent, and an angle comes out.

An angle goes into sine, and a trig ratio comes out.

In other words, the expression tan-1(5/12) represents an angle. So, the exercise asks for the sine of that angle.

You don't need to calculate the angle's measure. Just represent it on paper, by drawing a right triangle. Look at the ratio going into the arctangent function and then use the right-triangle definition for tangent to label the corresponding sides on your drawing. You can then determine the remaining side, followed by using the definition for sine to write the requested trig ratio. Cheers

?
 
Hello. Start by remembering what the arctangent and sine functions each input and output.

A trig ratio goes into arctangent, and an angle comes out.

An angle goes into sine, and a trig ratio comes out.

In other words, the expression tan-1(5/12) represents an angle. So, the exercise asks for the sine of that angle.

You don't need to calculate the angle's measure. Just represent it on paper, by drawing a right triangle. Look at the ratio going into the arctangent function and then use the right-triangle definition for tangent to label the corresponding sides on your drawing. You can then determine the remaining side, followed by using the definition for sine to write the requested trig ratio. Cheers

?
@Otis Alright. Thanks for the explanation! It makes sense now. ?
 
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