91Ó°ÊÓ

SOLVE. $$\cos ^{-1} x=\cos ^{-1} \frac{3}{5}-\sin ^{-1} \frac{4}{5}$$

Fill in the blank with the correct term. Some of the given choices will not be used. $$\begin{array}{ll}\text { linear speed } & \text { congruent } \\ \text { angular speed } & \text { circular } \\ \text { angle of elevation } & \text { periodic } \\ \text { angle of depression } & \text { period } \\ \text { complementary } & \text { amplitude } \\ \text { supplementary } & \text { quadrantal } \\ \text { similar } & \text { radian measure }\end{array}$$ Triangles are ________________ if their corresponding angles have the same measure.

Assuming that \(\sin \theta=0.6249\) and \(\cos \phi=0.1102\) and that both \(\theta\) and \(\phi\) are first-quadrant angles, evaluate each of the following. $$\tan (\theta+\phi)$$

Assuming that \(\sin \theta=0.6249\) and \(\cos \phi=0.1102\) and that both \(\theta\) and \(\phi\) are first-quadrant angles, evaluate each of the following. $$\sin (\theta-\phi)$$

SOLVE. $$\sin ^{-1} x=\tan ^{-1} \frac{1}{3}+\tan ^{-1} \frac{1}{2}$$

Fill in the blank with the correct term. Some of the given choices will not be used. $$\begin{array}{ll}\text { linear speed } & \text { congruent } \\ \text { angular speed } & \text { circular } \\ \text { angle of elevation } & \text { periodic } \\ \text { angle of depression } & \text { period } \\ \text { complementary } & \text { amplitude } \\ \text { supplementary } & \text { quadrantal } \\ \text { similar } & \text { radian measure }\end{array}$$ The angle between the horizontal and a line of sight below the horizontal is called a(n) __________.

Electrical Theory. In electrical theory, the following equations occur: $$E_{1}=\sqrt{2} E_{t} \cos \left(\theta+\frac{\pi}{P}\right)$$ and $$E_{2}=\sqrt{2} E_{t} \cos \left(\theta-\frac{\pi}{P}\right)$$. Assuming that these equations hold, show that $$\frac{E_{1}+E_{2}}{2}=\sqrt{2} E_{t} \cos \theta \cos \frac{\pi}{P}$$ and $$\frac{E_{1}-E_{2}}{2}=-\sqrt{2} E_{t} \sin \theta \sin \frac{\pi}{P}$$.

Fill in the blank with the correct term. Some of the given choices will not be used. $$\begin{array}{ll}\text { linear speed } & \text { congruent } \\ \text { angular speed } & \text { circular } \\ \text { angle of elevation } & \text { periodic } \\ \text { angle of depression } & \text { period } \\ \text { complementary } & \text { amplitude } \\ \text { supplementary } & \text { quadrantal } \\ \text { similar } & \text { radian measure }\end{array}$$ __________ is the amount of rotation per unit of time.

SOLVE. $$\text { Suppose that } \sin x=5 \cos x . \text { Find } \sin x \cos x$$

Fill in the blank with the correct term. Some of the given choices will not be used. $$\begin{array}{ll}\text { linear speed } & \text { congruent } \\ \text { angular speed } & \text { circular } \\ \text { angle of elevation } & \text { periodic } \\ \text { angle of depression } & \text { period } \\ \text { complementary } & \text { amplitude } \\ \text { supplementary } & \text { quadrantal } \\ \text { similar } & \text { radian measure }\end{array}$$ Two positive angles are ____________ if their sum is \(180^{\circ}\).