Use periodic properties of the trigonometric function to find the exact value of the expression. Tan 29pi/3

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Answer 1

Hi, Shaukat. Since Tan(x) has a period of pi, every time I add or take pi from Tan(x) I am left with the same value.

 

Pi can also be expressed as 3pi/3

So, Tan(29pi/3) = tan(29pi/3 - 3pi/3) = Tan(26pi/3)

 

If I repeat this process, I get:

Tan(29pi/3) = Tan(26pi/3) = Tan(23pi/3) = Tan(20pi/3) = Tan(17pi/3) = Tan(14pi/3) = Tan(11pi/3) = Tan(8pi/3) = Tan(5pi/3) = Tan(2pi/3)

 

When I get to Tan(2pi/3), I recall that it has a reference angle of pi/3. So, its absolute value is the same as that of Tan(pi/3), but due to its being in the second quadrant its sign is negative.

 

Tan(pi/3) = sqrt3, so Tan(2pi/3) = -sqrt3