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C2 Trigonometry, help?

Hi. I'm having trouble with this question.

How would I work out the smallest positive angle of these without a calculator? I can't find any resources with an explanation of how to do these.

Question -
Find the smallest positive angle which satisfies the following equation:
tan⁡ϕ\tan \phi = 13\frac{1}{3}3\sqrt 3

AND

sin⁡ϕ\sin \phi = 12\frac{1}{2}3\sqrt 3
(edited 9 years ago)
Original post by Peppercrunch
Hi. I'm having trouble with this question.

How would I work out the smallest positive angle of these without a calculator? I can't find any resources with an explanation of how to do these.

Question
Find the smallest positive angle which satisfies the following equation:
tan⁡ϕ\tan \phi = 13\frac{1}{3}3\sqrt 3

AND

sin⁡ϕ\sin \phi = 12\frac{1}{2}3\sqrt 3


There are a set of angles that you are meant to know the trig functions for
0,30,45,60,90
Original post by TenOfThem
There are a set of angles that you are meant to know the trig functions for
0,30,45,60,90


Oh ok, thank you. I didn't realise I could use them.

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