## Trigonometry 7th Edition

Case 1- When $\sin\theta$ and $\tan\theta$ both are positive By Definition I- $\sin\theta$ =$\frac{y}{r}$ Given $\sin\theta$ is positive, hence y is positive as r being distance can not be negative. 'y' is positive in Quadrant I and II. $\tan\theta$ =$\frac{y}{x}$ If y is positive, x also has to be positive for $\tan\theta$ to be positive. Thus x and y both are positive. Hence terminal side lies in Quadrant I. Case 2- When $\sin\theta$ and $\tan\theta$ both are negative By Definition I- $\sin\theta$ =$\frac{y}{r}$ Given $\sin\theta$ is negative, hence y is negative as r being distance can not be negative. 'y' is negative in Quadrant III and IV. $\tan\theta$ =$\frac{y}{x}$ If y is negative, x has to be positive for $\tan\theta$ to be negative. Thus x is positive and y is negative. Hence terminal side lies in Quadrant IV.