Chapter 13

Find the foci of each hyperbola. Draw the graph. $$ \frac{x^{2}}{36}-\frac{y^{2}}{49}=1 $$

For Exercises \(75-78,\) suppose \(\cos \theta=\frac{3}{5}\) and \(\sin \theta>0\) . Enter each answer as a fraction. What is \(\cot \theta ?\)

Find the foci of each hyperbola. Draw the graph. $$ \frac{x^{2}}{81}-\frac{y^{2}}{64}=1 $$

For Exercises \(75-78,\) suppose \(\cos \theta=\frac{3}{5}\) and \(\sin \theta>0\) . Enter each answer as a fraction. What is \(\csc \theta ?\)

For Exercises \(79-82,\) suppose tan \(\theta=\frac{4}{3}, \sin \theta>0,\) and \(-\frac{\pi}{2} \leq \theta<\frac{\pi}{2}\) . Enter each answer as a decimal. What is \(\cot \theta+\cos \theta ?\)

For Exercises \(79-82,\) suppose tan \(\theta=\frac{4}{3}, \sin \theta>0,\) and \(-\frac{\pi}{2} \leq \theta<\frac{\pi}{2}\) . Enter each answer as a decimal. What is \((\sin \theta)(\cot \theta) ?\)

For Exercises \(79-82,\) suppose tan \(\theta=\frac{4}{3}, \sin \theta>0,\) and \(-\frac{\pi}{2} \leq \theta<\frac{\pi}{2}\) . Enter each answer as a decimal. What is \(\sec \theta \div \tan \theta ?\)

For Exercises \(79-82,\) suppose tan \(\theta=\frac{4}{3}, \sin \theta>0,\) and \(-\frac{\pi}{2} \leq \theta<\frac{\pi}{2}\) . Enter each answer as a decimal. What is \(\sin \theta+\cos \theta+\cot \theta+\csc \theta ?\)

Find the amplitude and period of each function. Describe any phase shift and vertical shift in the graph. $$ y=2 \sin x-5 $$

Find the amplitude and period of each function. Describe any phase shift and vertical shift in the graph. $$ y=-\cos (x+4)-7 $$

Find the amplitude and period of each function. Describe any phase shift and vertical shift in the graph. $$ y=-3 \sin \left(x+\frac{\pi}{6}\right)+4 $$

Find the amplitude and period of each function. Describe any phase shift and vertical shift in the graph. $$ y=5 \cos \pi(x-1.5)-8 $$

Sketch a normal curve for each distribution. Label the \(x\) -axis values at one, two, and three standard deviations from the mean. mean \(=25,\) standard deviation \(=5\)

Sketch a normal curve for each distribution. Label the \(x\) -axis values at one, two, and three standard deviations from the mean. mean \(=25,\) standard deviation \(=10\)

Write and evaluate a sum to approximate the area under each curve for the domain \(-1 \leq x \leq 2 .\) a. Use inscribed rectangles 1 unit wide. b. Use circumscribed rectangles 1 unit wide. $$ f(x)=3 x^{2} $$

Write and evaluate a sum to approximate the area under each curve for the domain \(-1 \leq x \leq 2 .\) a. Use inscribed rectangles 1 unit wide. b. Use circumscribed rectangles 1 unit wide. $$ y=x^{2}+4 $$

Write and evaluate a sum to approximate the area under each curve for the domain \(-1 \leq x \leq 2 .\) a. Use inscribed rectangles 1 unit wide. b. Use circumscribed rectangles 1 unit wide. $$ g(x)=-x^{2}+4 $$

Write and evaluate a sum to approximate the area under each curve for the domain \(-1 \leq x \leq 2 .\) a. Use inscribed rectangles 1 unit wide. b. Use circumscribed rectangles 1 unit wide. $$ g(x)=-x^{2}+8 $$