Question

evaluate the expression cot(15°)

Answer 1

What are you allowed to use? A calculator?

Answer 2

cot A = 1/tan A

Answer 3

no I cant use a calculator i have to show my work

Answer 4

Can you find tan(30)?

Answer 5

Do you know the unit circle?

Answer 6

tan(30)=1/√3

Answer 7

do you know about the sum and difference trig functions...?

Answer 8

Now you can use the half angle formula for tan to get tan(15), Then cot(15) = 1/tan(15)

Answer 9

as cot = 1/tan

so you could take the reciprocal of

\[\cot(45 - 30) = \frac{1}{\tan((45 - 30)} = \frac{1 +\tan(45)\tan(30)}{\tan(45)-\tan(30)}\]

Answer 10

then use the exact value triangle for tan(45) and tan(30) then substitute

Answer 11

how do i find those exact values?

Answer 12

tan(A/2) = (1 - cosA)/(sin A)
If you use sin(30) and cos(30) in the formula above, you get tan(15)
Then do cot(15) = 1/tan(15)

Answer 13

well here are the triangles



hope this helps

Answer 14

remember tan = opp/adj

Answer 15

so im solving for tangent?

Answer 16

yep... in the left triangle what is the value of tan(45)

in the right triangle, what is the value of tan(30)

when you have them substitute them into the formula above..