1. ## Trigonometry

Find the value of x in fourth quadrant if $\displaystyle Tan x=-\sqrt{3}$

2. In the 4th quadrant consider $\displaystyle 2\pi-\theta$

Where $\displaystyle \theta = \frac{\pi}{3}$ is an angle on the triangle with $\displaystyle \tan(\theta) = \frac{O}{A} = \frac{\sqrt{3}}{1}$

$\displaystyle 2\pi-\frac{\pi}{3}= \dots$

3. The value of x is -60 when I used the calculator.After that I am lost cause tan is negative in fourth quadrant.

4. Originally Posted by roshanhero
Find the value of x in fourth quadrant if $\displaystyle Tan x=-\sqrt{3}$
The reference angle is 60 degree . So in the 4th quadrant :

360 -60 = 300 degree

in fact , tan 300 = tan (-60) because

tan(-60)=-(tan 60) = -(-tan 300)=tan 300

5. Originally Posted by roshanhero
The value of x is -60 when I used the calculator.After that I am lost cause tan is negative in fourth quadrant.

both -60 and 360-60 = 300 are the same angle and in the 4th quadrant.

-60 is going clockwise and 300 counter clockwise, you end up at the same point.