Find sin(x) and cos(x) if tan(x)=sqrt(3)

tanx = sqrt3 means x = 60 or 240,
So sin60 = (sqrt3)/2 and cos60 = 1/2
sin240 = - (sqrt3)/2 and cos240 = - 1/2, why should one need a calculator?

tan(x)=sqrt(3)
ie, x=60 degree
hence sin(x)=sqrt(3)/2
and cos(x)=1/2

Step 1: Pick up a graphics calculator.
Step 2: type in 'solve(tan(x)=sqrt(3),x)'
Step 4: press enter.
Step 5: times the answer (x) by Sin and Cos.
Step 6: write down answer and give to maths teacher.

Draw a right triangle

Tan (x) = sqrt3 /1 , so opposite side is sqrt3 and adjacent side is 1
Hypotenuse will be c^2 = 3+1= 4
c=2
so sin x= (1/2) sqrt3
cos x= 1/2

if tan(x) = sqrt(30)

then x = 60 < because tan(60)=sqrt(3) >

so sin(60) = sqrt(3) / 2

& cos(60) = 1/2

hence sin(x)=sqrt(3)/2 & cos(x)=1/2

sinα=[2tan(α/2)]/{1+[tan(α/2)]^2} 　　
cosα=[1-tan(α/2)^2]/{1+[tan(α/2)]^2} 　
tanα=[2tan(α/2)]/{1-[tan(α/2)]^2}