91Ó°ÊÓ

Find no angles in the interval \([0,2 \pi)\) that satisfy the given equation. Give calculator approximations to as many digits as your calculator displays. $$\cot \theta \approx 0.29949853$$

Find all trigonometric function values for each angle \(\boldsymbol{\theta}\). \(\cot \theta=\frac{\sqrt{3}}{8},\) given that \(\theta\) is in quadrant I

Approximate the area of a sector of a circle having radius \(r\) and central angle \(\boldsymbol{\theta}.\) $$r=29.2 \text { meters; } \theta=\frac{5 \pi}{6} \text { radians }$$

Find all trigonometric function values for each angle \(\boldsymbol{\theta}\). \(\csc \theta=2,\) given that \(\theta\) is in quadrant II

Find no angles in the interval \([0,2 \pi)\) that satisfy the given equation. Give calculator approximations to as many digits as your calculator displays. $$\csc \theta=1.0219553$$

Approximate the area of a sector of a circle having radius \(r\) and central angle \(\boldsymbol{\theta}.\) \(r=59.8\) kilometers \(; \theta=\frac{2 \pi}{3}\) radians

Find all trigonometric function values for each angle \(\boldsymbol{\theta}\). $$\sin \theta=\frac{\sqrt{2}}{6}, \text { given that } \cos \theta<0$$

Approximate the area of a sector of a circle having radius \(r\) and central angle \(\boldsymbol{\theta}.\) \(r=12.7\) centimeters; \(\theta=81.0^{\circ}\)

In a square window of your calculator that gives a good picture of the first quadrant, graph the line \(y=\sqrt{3} x\) with \(x \geq 0 .\) Then, trace to any point on the line. See the figure. What we see is the terminal side of a standard position angle in quadrant I. Store the values of \(\mathrm{X}\) and \(\mathrm{Y}\) in convenient memory locations, and call them \(\mathrm{X}_{1}\) and \(\mathrm{Y}_{1}\). Calculate the value of \(\sqrt{\mathrm{X}_{1}^{2}+\mathrm{Y}_{1}^{2}}\) and store it in a convenient memory location. (Call it \(r\) ) What does this number mean geometrically?

Find all trigonometric function values for each angle \(\boldsymbol{\theta}\). $$\cos \theta=\frac{\sqrt{5}}{8}, \text { given that } \tan \theta<0$$