91Ó°ÊÓ

Find the lengths of both circular arcs on the unit circle connecting the point \(\left(-\frac{\sqrt{3}}{2},-\frac{1}{2}\right)\) and the endpoint of the radius corresponding to \(20^{\circ}\).

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. $$ \cos (v-6 \pi) $$

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. $$ \sin (u-6 \pi) $$

What is the slope of the radius of the unit circle corresponding to \(30^{\circ}\) ?

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. $$ \sin (v+10 \pi) $$

What is the slope of the radius of the unit circle corresponding to \(60^{\circ}\) ?

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. $$ \tan (u+8 \pi) $$

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.] How many grads are in a right angle?

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. $$ \tan (v-4 \pi) $$

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.] The angles in a triangle add up to how many grads?