Question

Find the value of the following using the concepts of both addition and subtraction formulas and reference angle:

tan (-165)

Answer 1

tan(-165) = - tan(165) = - tan(180-165) = - ( -tan(15)) = tan 15

Answer 2

okay

Answer 3

= 2-(sqrt3)
?
@MonoPolyRoly

Answer 4

did i get it right?

Answer 5

Yes.

Answer 6

okay thanks @MonoPolyRoly :)

Answer 7

you could also just find
-tan(120+45) then use the angle sum formula

Answer 8

what's that?
i dont understand. really sorry @agent0smith

Answer 9

what's what...? " using the concepts of both addition and subtraction formulas" you're supposed to use angle sum formulas

Answer 10

Hmm, when he finds tan(15), can't he use tan(45-30) ?

Answer 11

oh i see now
@agent0smith
but was the answer that i found correct?

Answer 12

Yeah, i'm just saying you can skip a couple of steps. Same thing either way really... and it does say to use a reference angle.

Answer 13

You can have many ways to do this question...

Answer 14

could you please explain: - ( -tan(15))

i dont understand how this happened?
@MonoPolyRoly

Answer 15

tan(-165) = -tan(165) = -tan(120+45)
Use compound angle formula.
Note that tan(120) = - tan(180- 60) = - ( - tan(60) ). Here, you use reference angle.

Answer 16

Sorry, my mistake in my first comment here. It should be
tan(-165) = - tan(165) = - tan(180-15) = - ( -tan(15)) = tan 15
Note that tan(180-x) = -(tanx).

Answer 17

You may find this table helpful.

Answer 18

what happens now?
will the answer change @MonoPolyRoly

Answer 19

The answer won't change. It's just that I made a silly mistake in the part " - tan(165) = - tan(180-15)". I wrote " - tan(165) = - tan(180-165)", which was not correct, as tan(165) ≠ tan(180-165).

Answer 20

oh okay.