Chapter 7: Problem 47
Use a calculator to find the approximate value of each expression. Round the answer to two decimal places. $$ \tan 0.9 $$
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\(f(x)=\sin x, g(x)=\cos x, h(x)=2 x,\) and \(p(x)=\frac{x}{2} .\) Find the value of each of the following: $$ (f \circ h)\left(\frac{\pi}{6}\right) $$
\(f(x)=\sin x, g(x)=\cos x, h(x)=2 x,\) and \(p(x)=\frac{x}{2} .\) Find the value of each of the following: $$ (g \circ p)\left(60^{\circ}\right) $$
A point on the terminal side of an angle \(\theta\) in standard position is given. Find the exact value of each of the six trigonometric functions of \(\theta .\) $$ \left(-\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right) $$
Convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places. \(350^{\circ}\)
Problems \(63-66\) require the following discussion. Projectile Motion The path of a projectile fired at an inclination \(\theta\) to the horizontal with initial speed \(v_{0}\) is a parabola. See the figure. The range \(R\) of the projectile-that is, the horizontal distance that the projectile travels-is found by using the function $$ R(\theta)=\frac{2 v_{0}^{2} \sin \theta \cos \theta}{g} $$ where \(g \approx 32.2\) feet per second per second \(\approx 9.8\) meters per second per second is the acceleration due to gravity. The maximum height \(H\) of the projectile is given by the function $$ H(\theta)=\frac{v_{0}^{2} \sin ^{2} \theta}{2 g} $$ Find the range \(R\) and maximum height \(H\) of the projectile. Round answers to two decimal places. The projectile is fired at an angle of \(45^{\circ}\) to the horizontal with an initial speed of 100 feet per second.
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