Chapter 8.5, Problem 10CE

To determine

To explain: There is some angle whose tangent value is equal to 1,000,000. Also to determine any upper limit to tangent values.

Answer to Problem 10CE

Yes, there is some angle whose tangent value is 1,00,000 and the upper limit of θ will be less than 90°.

Explanation of Solution

It is known that $\tan \mathrm{\theta }=\frac{\mathrm{x}}{\mathrm{y}}$ .

Therefore, from this equation it is clear that there will be some angle.

When the value of $\text{x}$ is increased, y will be constant. When $\mathrm{\theta }$ increas es, $\text{x}$ also in creases and therefore tan\theta increases. The value of $\mathrm{\theta }$ can be increased to the upper limit of a value less than ${90}^{°}$ . At $=90$ , it will not behave as a triangle. So it is necessary to keep the value of $\mathrm{\theta }$ less than 90 .

  

Therefore, it can be concluded that there will be some angle for tangent values equal to 1,00,000 and in this, the value of x will be very high in comparison to y.