# Math Help - Solving Trigonometric Equations

1. ## Solving Trigonometric Equations

Given that sinx = 1/2, cos x = (rt.3)/2 and 0 degrees less than or equal x less than or equal 360 degrees,
a) Find the values of x
b) write down the exact value of tan x.

My solution is...
a) x = 30, 150, 330
but the book only says that 30 degrees is the solution... am I right? or is the book right?

b) I have two exact values for tanx: 1/(rt.3) and -1/(rt.3)
but the book has it down as: (rt.3)/3

Are my answers correct?

2. Originally Posted by bhuang
Given that sinx = 1/2, cos x = (rt.3)/2 and 0 degrees less than or equal x less than or equal 360 degrees,
a) Find the values of x
b) write down the exact value of tan x.

My solution is...
a) x = 30, 150, 330
but the book only says that 30 degrees is the solution... am I right? or is the book right?

b) I have two exact values for tanx: 1/(rt.3) and -1/(rt.3)
but the book has it down as: (rt.3)/3

Are my answers correct?
For the first one, both sin and cos are positive there will only be one solution and it will be in the first quadrant (ie 30 degrees).
cos 150 is negative, and sin 330 is negative so are not solutions. The book is correct!

3. Originally Posted by Debsta
For the first one, both sin and cos are positive there will only be one solution and it will be in the first quadrant (ie 30 degrees).
cos 150 is negative, and sin 330 is negative so are not solutions. The book is correct!
For the second one, since tan x = sin x/cos x and bothe sin x and cos x are positive (as given) then tan x must also be positive. So the solution is 1/(rt 3). (Note that this is the same as (rt 3) /3 when the denominator is rationalised.