SOLUTION: Hi, Find the general solution of tanƟ =-√3 and find solutions when n=1 and n=2. Thank you

Algebra ->  Trigonometry-basics -> SOLUTION: Hi, Find the general solution of tanƟ =-√3 and find solutions when n=1 and n=2. Thank you      Log On


   

Question 1202952: Hi,
Find the general solution of tanƟ =-√3 and find solutions when n=1 and n=2.
Thank you
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

I'll assume you are working in radian mode.

Use the unit circle to go from
tan%28theta%29+=+-sqrt%283%29
to
theta+=+2pi%2F3+%2B+pi%2An

When n = 1, then,
theta+=+2pi%2F3+%2B+pi%2An

theta+=+2pi%2F3+%2B+pi%2A1

theta+=+2pi%2F3+%2B+pi

theta+=+2pi%2F3+%2B+pi%2A%283%2F3%29

theta+=+2pi%2F3+%2B+3pi%2F3

theta+=+%282pi%2B3pi%29%2F3

theta+=+%285pi%29%2F3

theta+=+5.235988 (approximate)


When n = 2, then,
theta+=+2pi%2F3+%2B+pi%2An

theta+=+2pi%2F3+%2B+pi%2A2

theta+=+2pi%2F3+%2B+2pi

theta+=+2pi%2F3+%2B+2pi%2A%283%2F3%29

theta+=+2pi%2F3+%2B+6pi%2F3

theta+=+%282pi%2B6pi%29%2F3

theta+=+%288pi%29%2F3

theta+=+8.37758 (approximate)

You can use graphing software such as Desmos or GeoGebra to confirm these solutions. Spreadsheet software works as well.