Trigonometric Functions
Examples:
1. Given that \(\sin \theta = \frac{3}{5}\), and \(\theta\)
is an acute angle, find the exact value of each of the remaining five
trigonometric functions of \(\theta\). SOLUTION
2. Find the exact value of each expression. Do not use a
calculator. SOLUTION
(a) \(\displaystyle{\tan 10^\circ -\frac{\sin
10^\circ}{\cos 10^\circ}}\) (b) \(\displaystyle{\cos^2
\frac{\pi}{5} +\frac{1}{\csc^2 \frac{\pi}{5}}}\) (c)
\(\displaystyle{\sec^2 40^\circ - \tan^2 40^\circ}\)
(d) \(\displaystyle{\tan 10^\circ \cos 10^\circ \csc 10^\circ}\)
3. The builder of a parking garage wants to build a ramp
that meets the ground at \(30^\circ\). If the horizontal span covers
\(30\) feet, how long is the ramp? SOLUTION
4. Find the exact value of each of the remaining trigonometric functions of \(\theta\) if \(\displaystyle{\sin\theta = \frac{12}{13}} \) and \(\displaystyle{\tan \theta < 0 } \). SOLUTION
5. Answer the following. SOLUTION
(a) Given that \(\cos\theta=\dfrac{2}{3}\). Find the exact
value of \( \cos\theta + \cos(\theta+2\pi) + \cos(\theta+4\pi)\quad \)
(b) Given that \(\cot\theta= -2\). Find the exact value of \( \cot\theta + \cot(\theta-\pi) + \cot(\theta-2\pi)\quad \)