91Ó°ÊÓ

Because of seasonal changes in vegetation, carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) levels, as a product of photosynthesis, rise and fall during the year. Besides the naturally occurring \(\mathrm{CO}_{2}\) from plants, additional \(\mathrm{CO}_{2}\) is given off as a pollutant. A reasonable model of \(\mathrm{CO}_{2}\) levels in a city for the years \(1982-2002\) is given by \(y=2.3 \sin 2 \pi t+1.25 t+315,\) where \(t\) is the number of years since 1982 and \(y\) is the concentration of \(\mathrm{CO}_{2}\) in parts per million (ppm). Find the difference in \(\mathrm{CO}_{2}\) levels between the beginning of 1982 and the beginning of 2002

Use the fundamental trigonometric identities to write each expression in terms of a single trigonometric function or a constant. $$\frac{\sec ^{2} t}{\tan t}$$

Write an equation that is of the form \(y=\tan b x, y=\cot b x, y=\sec b x,\) or \(y=\csc b x\) and satisfies the given conditions. Cosecant, period: \(\frac{5 \pi}{2}\)

A pulley with a diameter of 1.2 meters uses a belt to drive a pulley with a diameter of 0.8 meter. The 1.2 -meter pulley turns through an angle of \(240^{\circ} .\) Find the angle through which the 0.8 -meter pulley turns.

Use a graphing utility to graph each function. $$y=3^{\cos ^{2} x} \cdot 3^{\sin ^{2} x}$$

Use a graphing utility to graph each function. $$y=\cos |x|$$

Use the fundamental trigonometric identities to write each expression in terms of a single trigonometric function or a constant. $$1-\sec ^{2} t$$

Find the angular speed, in radians per second, of the second hand on a clock.

Write an equation that is of the form \(y=\tan b x, y=\cot b x, y=\sec b x,\) or \(y=\csc b x\) and satisfies the given conditions. Cotangent, period: 2

Use the fundamental trigonometric identities to write each expression in terms of a single trigonometric function or a constant. $$1-\csc ^{2} t$$