91Ó°ÊÓ

Use the following information for Problems \(60-65:\) A grad is a unit of measurement for angles that is sometimes used in surveying, especially in some European countries. A complete revolution once around a circle is 400 grads. [These problems may help you work comfortably with angles in units other than degrees. In the next section we will introduce radians, the most important units used for angles.] Each angle of an equilateral triangle has how many grads?

Suppose \(u\) and \(v\) are in the interval \(\left(\frac{\pi}{2}, \pi\right),\) with $$ \tan u=-2 \text { and } \tan v=-3 $$ Find exact expressions for the indicated quantities. $$ \cos (v+5 \pi) $$

Suppose \(u\) and \(v\) are in the interval \(\left(\frac{\pi}{2}, \pi\right),\) with $$ \tan u=-2 \text { and } \tan v=-3 $$ Find exact expressions for the indicated quantities. $$ \sin (u+5 \pi) $$

Use the following information for Problems \(60-65:\) A grad is a unit of measurement for angles that is sometimes used in surveying, especially in some European countries. A complete revolution once around a circle is 400 grads. [These problems may help you work comfortably with angles in units other than degrees. In the next section we will introduce radians, the most important units used for angles.] Convert \(37^{\circ}\) to grads.

Use the following information for Problems \(60-65:\) A grad is a unit of measurement for angles that is sometimes used in surveying, especially in some European countries. A complete revolution once around a circle is 400 grads. [These problems may help you work comfortably with angles in units other than degrees. In the next section we will introduce radians, the most important units used for angles.] Convert 37 grads to degrees.

Suppose \(u\) and \(v\) are in the interval \(\left(\frac{\pi}{2}, \pi\right),\) with $$ \tan u=-2 \text { and } \tan v=-3 $$ Find exact expressions for the indicated quantities. $$ \tan (u-9 \pi) $$

Verify that each of the following points is on the unit circle. (a) \(\left(\frac{3}{5}, \frac{4}{5}\right)\) (b) \(\left(\frac{5}{13}, \frac{12}{13}\right)\) (c) \(\left(\frac{8}{17}, \frac{15}{17}\right)\)

Suppose \(u\) and \(v\) are in the interval \(\left(\frac{\pi}{2}, \pi\right),\) with $$ \tan u=-2 \text { and } \tan v=-3 $$ Find exact expressions for the indicated quantities. $$ \tan (v+3 \pi) $$

Show that if \(m\) and \(n\) are integers, not both zero, then $$ \left(\frac{m^{2}-n^{2}}{m^{2}+n^{2}}, \frac{2 m n}{m^{2}+n^{2}}\right) $$ is a point on the unit circle.

Suppose \(u\) and \(v\) are in the interval \(\left(\frac{\pi}{2}, \pi\right),\) with $$ \tan u=-2 \text { and } \tan v=-3 $$ Find exact expressions for the indicated quantities. $$ \cos \left(\frac{\pi}{2}-u\right) $$