Question

solve for cot(2theta/3)=squareroot of 3

Answer 1

If you realize mebbe that cot(n)=1/tan(n), and thus tan(2θ/3)=1/√(3), 2θ/3=arctan(1/√(3)), or θ=(3/2)arctan(1/√(3)). Which should be solvable via the miracle known as the calculator.

Answer 2

we r not allowed to use calculator

Answer 3

Awright. The angle is 30 degrees. Memorize that.

Answer 4

what can u show me step by step
please

Answer 5

cot(2θ/3)=√(3); solve for θ
1/tan(2θ/3)=√(3); definition of cotangent
tan(2θ/3)=1/√(3); raise both sides to the power of -1
2θ/3=arctan(1/√(3)); take the arctan of both sides
θ=(3/2)arctan(1/√(3)); multiply both sides by 3/2
θ=(3/2)(π/6); remember that arctan(1/√(3)) is (π/6) or 30°
θ=π/4

Answer 6

The last step is obviously a simplification.

Answer 7

what is arctan

Answer 8

The inverse tangent; it's easier to write it as such on OpenStudy.

Answer 9

so arctan is the same as cotangent?

Answer 10

No. Let's say I had y=tan(x), okay? 1/y=1/tan(x)=cot(x). However, x=arctan(y).

Answer 11

is there another way to solve without using arctan cause im supposed to use the trig identities

Answer 12

Yes, there's another way without trig identities. It looks exactly the same, except instead of taking the arctan of both sides, you pretend there's no arctan, and just memorize all the steps in between.

Answer 13

no with identities and without arctan

Answer 14

Arctan is a basic trig identity. It's the functional inverse of tan. As I said, if your teacher hasn't mentioned arctan yet, it's because s/he wants you to do it WITH arctan but pretend it isn't there.

Answer 15

okay