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Let x be an acute angle such that tan(x) = 1/3.  Find sin(x) + cos(x).

 May 11, 2020
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Draw the picture in the first quadrant.

 

Since  tan(x)  =  opposite / adjacent  =  1 / 3,

the opposite side  =  1     and     the adjacent side  =  3

 

Using the Pythagorean Theorem:  hypotenuse2  =  opposite2  +  adjacent2

                                                                              =  12 + 32  =  10

                                                         hypotenuse  =  sqrt(10)

 

sin(x)  =  opposite / hypotenuse  =  1 / sqrt(10)

cos(x)  =  adjacent / hypotenuse  =  3 / sqrt(10)

 

You should place each of these answers in simplest radical form.

 May 11, 2020

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