Exam 4: Trigonometric Functions of Angles

Find the exact length of the arc subtended by a central angle of $\theta$ = 30° on a circle with radius 3 cm.

An engineer wants to construct a bridge across a fast moving river. Using a straight line segment between two points that are 187 feet apart along his side of the river, he measures the angles formed when sighting the point on the other side where he wants to have the bridge end. If the angles formed at points A and B are 68° and 34°, respectively, how far is it from point B to the point on the other side of the river? Round to one decimal place.

Determine the angle of the smallest possible positive measure that is coterminal with the given angle.

Determine the angle of the smallest possible positive measure that is coterminal with 1348°.

Gears. Two gears have interlocking teeth, which cause them to rotate in opposite directions. The smaller (pinion) gear has a radius of 8 mm and the larger (spur) gear has a radius of 13 mm. If the pinion gear rotates 83°, how many degrees will the spur gear rotate? Round your answer to the nearest degree.

Find all values of $\theta$ , where 0° $\le$ 360° when tan $\theta$ = - 1.

The terminal side of an angle θ in standard position passes through the point . Calculate the exact value of cot θ.

A plane flew due north at 460 mph for 3.5 hours. A second plane, starting at the same point and at the same time flew southeast at an angle 140° clockwise from due north for 3.5 hours. If, at the end of the 3.5 hours, the two planes were 2550 miles apart, how fast was the second plane traveling?

Find the exact length of the arc subtended by a central angle of θ = 900° on a circle with radius 5 ft.

The terminal side of an angle θ in standard position passes through the point (-6, 1). Calculate the value of cosθ. Round your answer to four decimal places.

Find the exact length of the arc subtended by a central angle of $\theta$ = 17 on a circle with radius 13 ft.

Height of a sequoia tree. Sequoias are among the longest living trees in the world. They can grow to a maximum height of 311 ft and can live up to 3,200 years. A park ranger wants to determine the height of a sequoia tree without having to climb to the top of it. He measures the length of the tree's shadow and determines the angle of elevation from the tip of the shadow to the top of the tree. Using this information and a trigonometric function, the park ranger can calculate the height of the tree. What is the height of a tree if its shadow is 253 ft long and the angle of elevation is 43°? Round your answer to one decimal place. 43° 253 ft

Find the measure (in radians) of a central angle, $\theta$ , that intercepts an arc on a circle with radius 2.4 yds and arc length 1.4 yds.

The terminal side of an angle θ in standard position passes through the point . Calculate the exact value of cot θ.

Convert 104.1° to radians. Round your answer to 3 significant digits.

Find the area of the triangle described. Round to three decimal places. b = , c = , $\gamma$ = 54

Find all values of θ, where 0°< θ 360° when cosθ = .

Find the exact length of the arc subtended by a central angle of $\theta$ = On a circle with radius 22 yd.

A regular decagon has sides measuring 38 inches. What is its area? (Hint: The measure of an angle of a regular n-gon is equal to 180(n - 2) divided by the number of sides, n.) Round to one decimal place.

Find the linear speed of a point traveling at a constant speed along the circumference of a circle with radius r = 18 yards and angular velocity = .