Question

How do I solve tangent equations? The way my book describes it is...too complex. I even put an example but if you answer please describe every step so I can reuse the instructions.

tan(2π/3)=?

Answer 1

\(\huge \frac{\sin 2\pi/3}{\cos 2\pi/3}=?\)

Answer 2

Can you explain how to calculate the sin and cos...? I need everything explained or I won't get it :'I

Answer 3

\[\tan \left( \frac{ 2\pi }{3 } \right)=\tan \left( \pi-\frac{ \pi }{ 3 } \right)=-\tan \frac{ \pi }{ 3 }\]
\[=-\frac{ \sin \frac{ \pi }{3} }{\cos \frac{ \pi }{3 } }=-\frac{ \frac{ \sqrt{3} }{2 } }{\frac{ 1 }{2 } }\]
\[=-\frac{ \sqrt{3} }{2 }*\frac{ 2 }{ 1 }=-\sqrt{3}\]

Answer 4

\[\tan \left( \pi-\theta \right)=-\tan \theta \]

Answer 5

what exactly is the question?

Answer 6

I guess I don't understand how we went from the sin and cos values to the ones given across the equals sign. Is there something before this that needs to be understood before I tackle this?

Answer 7

\[\sin \frac{ 2\pi }{ 3 }=\sin \left( \pi-\frac{ \pi }{3} \right)=\sin \frac{ \pi }{ 3 }=\frac{ \sqrt{3} }{ 2}\]
\[\sin \left( \pi-\theta \right)=sin\theta \]
\[\cos \left( \pi-\theta \right)=\cos \theta \]
\[\cos \frac{ 2\pi }{ 3 }=\cos \left( \pi-\frac{{\pi } }{ 3} \right)=-\cos \frac{ \pi }{ 3 }=-\frac{ 1 }{2 }\]

Answer 8

There are a few angles for which people memorize the sin, cos and tan
(the sin (or cos or tan) of most angles is an ugly number)

you should know the sin, cos and tan of
sin cos tan
0º 0 1 0
30º 1/2 \(\sqrt{3}/2\) \(1/\sqrt{3} \)
45º \(\sqrt{2}/2\) \(\sqrt{2}/2\) 1
60º \(\sqrt{3}/2\) 1/2 \(\sqrt{3}\)
90º 1 0 \(\infty\)

Answer 9

you should also know how to translate between degrees and radians

(multiply radians by 180/pi to get degrees)

\(2\pi/3 \text{ rads} =2\pi/3 \cdot 180/\pi \text{ deg }= 120º \)

Answer 10

you should know about the "unit circle" so you can figure out angles bigger than 90º

Answer 11

there is a correction
\[\cos \left( \pi-\theta \right)=-\cos \theta \]

Answer 12

See
http://www.khanacademy.org/math/trigonometry/basic-trigonometry/unit_circle_tut/v/unit-circle-definition-of-trig-functions-1

for how to use the unit circle.

Answer 13

The way I would answer
tan(2pi/3) is (because I think in degrees) translate this to
tan(120º)

then I would sketch the angle 120º, starting at the x-axis and going counter-clockwise