Question

evalualte csc(pi/3)cot(pi/3)sin(pi/6)
help pleasee :D

Answer 1

csc(pi/3)=csc(60)

sin(60)=a√3 / 2a = √3 / 2 (you just have to draw a 30-60-90 triangle and write the correct proportions then solve for sin 60 to do find sin 60)

cos(60) = 1 / sin(60) = 1 / (√3 / 2) = 1 × (2 / √3 ) = 2 / √3 = 2√3 / 3

Answer 2

OK,

cot(60)= 1/ tan(60).
(draw a 30-60-90 triangle with correct proportions, (a , a√3 and 2a ) and find tan 60, using SOHCAHTOA, you will see that it is equal to opp/adj= a√3 / a = √3 )

Answer 3

and
sin(pi/6)= sin 30 = a/2a = 1/2 (also by drawing a 30-60-90 triangle )

Answer 4

So,
csc(pi/3)cot(pi/3)sin(pi/6) = (2√3 / 2 ) × ( √3) × (1/2) =( (2√3 / 2 ) × ( √3 / 1) × (1/2)

multiply tops and bottoms

2√3 × √3 × 1 6
------------ = ---- = 3 / 2
2 × 1 × 2 4

Answer 5

thanks

Answer 6

You welcome !