91Ó°ÊÓ

Calculate cot \(54.9^{\circ}\) in the following two ways: a. Find tan \(54.9^{\circ}\) to three decimal places and then divide 1 by that number. Write that number to five decimal places. b. With a calculator in degree mode, enter \(54.9,\) tan, \(1 / \mathrm{x},\) and round the result to five decimal places.

Find the angular speed (radians/second) associated with rotating a central angle \(\theta\) in time \(t\). $$\theta=25 \pi, t=10 \mathrm{sec}$$

Determine whether each statement is true or false. \(\cos \theta=\cos \left(\theta+360^{\circ} n\right),\) where \(n\) is an integer.

Calculate sec \(18.6^{\circ}\) in the following two ways: a. Find \(\cos 18.6^{\circ}\) to three decimal places and then divide 1 by that number. Write that number to five decimal places. b. With a calculator in degree mode, enter \(18.6, \cos , 1 / \mathrm{x},\) and round the result to five decimal places.

Find the angular speed (radians/second) associated with rotating a central angle \(\theta\) in time \(t\). $$\theta=\frac{3 \pi}{4}, t=\frac{1}{6} \mathrm{sec}$$

Determine whether each statement is true or false. \(\sin \theta=\sin (\theta+2 \pi n),\) where \(n\) is an integer.

If the terminal side of angle \(\theta\) passes through the point \((-3 a, 4 a),\) find \(\cos \theta .\) Assume \(a>0\)

In calculus, the value of \(F(b)-F(a)\) of a function \(F(x)\) at \(x=a\) and \(x=b\) plays an important role in the calculation of definite integrals. Find the exact value of \(F(b)-F(a)\). $$F(x)=\sec x, a=\frac{\pi}{6}, b=\frac{\pi}{3}$$

Find the angular speed (radians/second) associated with rotating a central angle \(\theta\) in time \(t\). $$\theta=200^{\circ}, t=5 \mathrm{sec}$$

If the terminal side of angle \(\theta\) passes through the point \((-3 a, 4 a),\) find \(\sin \theta .\) Assume \(a>0\)