How do you find the exact value of tan300?

2 Answers
Alan P.
Nov 9, 2016

tan(300^circ)=color(green)(-sqrt(3))

Explanation:

300^circ is equivalent to (-60^circ)
A 60^circ right triangle is one of the standard triangles.
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tan = "opposite"/"adjacent"

Cesareo R.
Nov 9, 2016

tan(300^@) = -sqrt(3)

Explanation:

300^@=360^@-60^@ equivalently we have
2pi-pi/3 = 300^@/180^@ pi then
tan(300^@)=tan(2pi-pi/3) but tan is periodic with period pi so
tan(2pi-pi/3)=tan(-pi/3) and tan is an odd function so
tan(-pi/3)=-tan(pi/3)
Now tan(x)=sin(x)/cos(x) and sin(pi/3)=1/2 so
cos(x)=sqrt(1-cos^2(x)) = sqrt(1-1/4)=sqrt(3)/2

Finally

tan(300^@) = -sqrt(3)

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