Question and Answers Forum

All Questions      Topic List

Trigonometry Questions

Previous in All Question      Next in All Question      

Previous in Trigonometry      Next in Trigonometry      

Question Number 21241 by tawa tawa last updated on 17/Sep/17

$$\mathrm{Find}\mathrm{y}\mathrm{in}3\mathrm{rd}\mathrm{quadrant}$$$$\tan (\mathrm{y}-30)=\cot \left(\mathrm{y}\right)$$

Answered by sma3l2996 last updated on 17/Sep/17

$$tan(y-30)=cot\left(y\right)$$$$tan(y-30)=\frac{1}{tan\left(y\right)}\iff \frac{tan\left(y\right)-tan\left(30\right)}{1+tan\left(y\right)tan\left(30\right)}=\frac{1}{tany}$$$$withtan\left(30\right)=\frac{\sqrt{3}}{3}$$$$tan\left(y\right)(tan\left(y\right)-tan\left(30\right))=1+tan\left(y\right)tan\left(30\right)$$$${tan}^2\left(y\right)-\frac{\sqrt{3}}{3}tan\left(y\right)-\frac{\sqrt{3}}{3}tan\left(y\right)=1$$$${tan}^2\left(y\right)-2\frac{\sqrt{3}}{3}tan\left(y\right)-1=0$$$$\mathrm{\Delta }=\frac{4}{3}+4=\frac{16}{3}={\left(\frac{4\sqrt{3}}{3}\right)}^2$$$$tan\left(y\right)=\frac{\frac{2\sqrt{3}}{3}-\frac{4\sqrt{3}}{3}}{2}=\frac{-\sqrt{3}}{3}\iff y=-\frac{\pi }{6}+k\pi$$$$ortan\left(y\right)=\frac{\frac{2\sqrt{3}}{3}+\frac{4\sqrt{3}}{3}}{2}=\sqrt{3}\iff y=\frac{\pi }{3}+k\pi$$$$$$

Commented by tawa tawa last updated on 17/Sep/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com