Simplify each trigonometric expression.
1) \(\Large\frac{\sin x}{\cos x}\)
2) \(\Large\frac{\cos x}{\sin x}\)
3) \(\Large\frac{\sin^{2}x +\cos^2x}{\cos x}\)
4) \(1 - \sin^2 x\)
5) \(1 - \cos^2 x\)
6) \(\Large\frac{\tan \theta}{\sec \theta}\)
7) \(\Large\frac{\cot \theta}{\csc \theta}\)
8) \(\Large\frac{\cos^2\theta + \sin^2\theta}{\sin x}\)
Approximate the trig ratio
9) If \(\sin (37^{\circ})\approx 0.6018\), then \(\sin(-37^{\circ})\approx\) ?
10) If \(\cos (89^{\circ})\approx 0.0174\), then \(\sin(1^{\circ})\approx\) ?
11) If \(\sin (-81^{\circ})\approx -0.9877\), then \(\sin(81^{\circ})\approx\) ?
12) If \(\cos (-67^{\circ})\approx 0.3907\), then \(\cos(67^{\circ})\approx\) ?
13) If \(\sin (12^{\circ})\approx 0.2079\), then \(\cos(-78^{\circ})\approx\) ?
14) If \(\cos (36^{\circ})\approx 0.8090\), then \(\sin(-54^{\circ})\approx\) ?
Review
15) Write the next four terms of the series: \(5 + \Large\frac{5}{8} + \frac{5}{27} + \frac{5}{64}+ ...\)
16) Write the series in summation notation: \(5 + \Large\frac{5}{8} + \frac{5}{27} + \frac{5}{64}+ ...\)
17) Write an explicit formula for the arithmetic sequence with \(a_4 = 17\) and \(a_7 = 140\).
18) Solve for \(x\): \(\left(\Large\frac{1}{3}\right)^{x-7}= 81^{x+5}\).
Solution Bank