91Ó°ÊÓ

Geometry The hypotenuse of a right triangle has a length of 8 inches. If one angle is \(35^{\circ}\), find the length of each leg.

Convert each angle to a decimal in degrees. Round your answer to two decimal places.\(40^{\circ} 10^{\prime} 25^{\prime \prime}\)

Convert each angle to a decimal in degrees. Round your answer to two decimal places. \(61^{\circ} 42^{\prime} 21^{\prime \prime}\)

Given \(\sec \theta=3,\) use trigonometric identities to find the exact value of (a) \(\cos \theta\) (b) \(\tan ^{2} \theta\) (c) \(\csc \left(90^{\circ}-\theta\right)\) (d) \(\sin ^{2} \theta\)

Given \(\cot \theta=2,\) use trigonometric identities to find the exact value of (a) \(\tan \theta\) (b) \(\csc ^{2} \theta\) (c) \(\tan \left(\frac{\pi}{2}-\theta\right)\) (d) \(\sec ^{2} \theta\)

Find the exact value of each expression. Do not use a calculator. $$ \cos \left(-45^{\circ}\right) $$

What is the domain of the sine function?

If \(\sin \theta=0.3,\) find the exact value of \(\sin \theta+\cos \left(\frac{\pi}{2}-\theta\right)\) Find an acute angle \(\theta\) that satisfies the equation

In blood spatter analysis, the width, \(w,\) and the length, \(L,\) of a blood stain from a blood droplet are related to the impact angle, \(\theta,\) by the equation \(\sin \theta=\frac{w}{L}\) If \(\tan \theta=\frac{17}{10}\) and the width of a droplet stain is \(4 \mathrm{~mm},\) what is the approximate length of the stain?

Hot-air Balloon While taking a ride in a hot-air balloon in Napa Valley, Francisco wonders how high he is. To find out, he chooses a landmark that is to the east of the balloon and measures the angle of depression to be \(54^{\circ} .\) A few minutes later, after traveling 100 feet east, the angle of depression to the same landmark is determined to be \(61^{\circ}\). Use this information to determine the height of the balloon.