1. Trigonometric Functions and Identities – Video Lesson Watch Video (opens YouTube in new tab)
2. Unit Circle and Trig Values – Video Lesson Watch Video (opens YouTube in new tab)
3. Find the value of the following trig functions. View Solution (a) \(\cot 0\)   (b) \(\sec\dfrac{\pi}{4}\)   (c) \(\csc\dfrac{\pi}{6}\)   (d) \(\sec\dfrac{\pi}{3}-\cot\dfrac{\pi}{4}\)   (e) \(\cos\dfrac{7\pi}{6}-\dfrac{1}{2}\cot\dfrac{5\pi}{6}\)
4. Find the exact value of each of the following trig functions. View Solution (a) \(\tan\dfrac{9\pi}{4}\)   (b) \(\cos\dfrac{19\pi}{6}\)   (c) \(\sin\dfrac{11\pi}{4}\)   (d) \(\sec\dfrac{10\pi}{3}\)   (e) \(\csc\dfrac{17\pi}{3}\)
5. Find the exact value of each of the following expressions. View Solution (a) \(\tan 40^{\circ}\cdot\dfrac{\csc 40^{\circ}}{\cos 40^{\circ}}\cdot\dfrac{1}{\sec^{2}40}\)   (b) \(\left(\sin\dfrac{\pi}{5}+\cos\dfrac{\pi}{5}\right)\tan\!\left(-\dfrac{\pi}{5}\right)\)
6. Find the exact value of each of the following expressions. View Solution (a) \(\tan 10^\circ-\dfrac{\sin 10^\circ}{\cos 10^\circ}\)   (b) \(\cos^{2}\dfrac{\pi}{5}+\dfrac{1}{\csc^{2}\frac{\pi}{5}}\)   (c) \(\sec^{2}40^\circ-\tan^{2}40^\circ\)   (d) \(\tan 10^\circ\cos 10^\circ\csc 10^\circ\)
7. Evaluate each expression without using a calculator. View Solution (a) \(2\sec(\pi/3)-\tan(3\pi/4)\)   (b) \(2\tan(\pi/4)-\dfrac{1}{2\tan(-5\pi/4)}+\sin(5\pi/6)\)
8. Evaluate each expression without using a calculator. View Solution (a) \(\tan(-7\pi/4)\cdot\cos(4\pi/3)-\sin(5\pi/6)\cdot\sin(3\pi/2)\)   (b) \(\sin(7\pi/6)+\cos(-\pi/3)-\csc^{2}(\pi/2)\)
9. Simplify the trigonometric expressions. View Solution (a) \(\cos\theta\cdot\csc\theta\cdot\tan\theta\)   (b) \(\sec\theta-\sec\theta\sin^{2}\theta\)   (c) \((\sin\theta+\cos\theta)^{2}+(\sin\theta-\cos\theta)^{2}\)
10. Simplify the trigonometric expressions. View Solution (a) \(\dfrac{\sin\theta-\sin^{3}\theta}{\cos^{2}\theta}\)   (b) \(1-\dfrac{\sin^{2}\theta}{1+\cos\theta}\)
11. Simplify the trigonometric expressions. View Solution (a) \(\tan\theta+\dfrac{\cos\theta}{1+\sin\theta}\)   (b) \(\dfrac{1-\cos\theta}{\sin\theta}+\dfrac{\sin\theta}{1-\cos\theta}\)
12. Find the exact value of each expression in radians. View Solution (a) \(\sin^{-1}(1)\)   (b) \(\sin^{-1}\!\left(\dfrac{1}{2}\right)\)   (c) \(\cos^{-1}(0)\)   (d) \(\tan^{-1}(1)\)   (e) \(\cos^{-1}(-1)\)
13. Find the exact value of each expression in radians. View Solution (a) \(\tan^{-1}\!\left(-\sqrt{3}\right)\)   (b) \(\sin^{-1}\!\left(-\dfrac{1}{2}\right)\)   (c) \(\tan^{-1}\!\left(\dfrac{\sqrt{3}}{3}\right)\)   (d) \(\cos^{-1}\!\left(\dfrac{\sqrt{3}}{2}\right)\)
14. Find the exact value of each expression in radians. View Solution (a) \(\sin^{-1}\!\left(\sin\dfrac{\pi}{5}\right)\)   (b) \(\cos^{-1}\!\left(\cos\dfrac{5\pi}{6}\right)\)   (c) \(\sin^{-1}\!\left(\tan\dfrac{3\pi}{4}\right)\)   (d) \(\tan^{-1}\!\left(\tan\dfrac{\pi}{7}\right)\)
15. Solve each equation on the interval \(0\leq\theta<2\pi\). View Solution (a) \(1-\cos\theta=\dfrac{1}{2}\)   (b) \(2\sin\theta+\sqrt{3}=0\)   (c) \(2\cos\theta-\sqrt{2}=0\)   (d) \(\sqrt{3}\tan\theta+3=0\)
16. Solve each equation on the interval \(0\leq\theta<2\pi\). View Solution (a) \(4\cos^{2}\theta-3=0\)   (b) \(2\sin^{2}\theta-1=\sin\theta\)