Exam 4: Trigonometric Functions of Angles

Use a calculator to approximate the tan 77.3° to three decimal places.

State in which quadrant or on what axis the terminal side of a 1271° angle in standard position lies.

If tan $\theta$ = , and the terminal side of $\theta$ lies in quadrant II, find cos $\theta$ .

Use a calculator to approximate the sin 69.3° to three decimal places.

Use the right triangle diagram below and the information given to find the indicated measure. α = 37°, a = 12 cm, find c. Round your answer to two decimal places.

Find the angular speed, , associated with rotating a central angle θ = 360° in time t = 20 seconds.

Use a calculator to approximate the cot 87.6° to three decimal places.

Find the linear speed of a point that moves with constant speed in a circular motion if the point travels along the circle an arc length s = 10 centimeters in time t = 6.5 minutes. Round your answer to two decimal places.

Find all values of $\theta$ , where 0° $\le$ 360° when sin $\theta$ =

Use a calculator to approximate the length of the arc on a circle with central angle θ = 125° and radius r = 22 km. Round your answer to the nearest integer.

Convert 46 degrees to radians. Round numbers to two decimal places and leave the answer in terms of π.

Find the area of the circular sector with a radius r = 7.8 ft and central angle θ = . Round your answer to three significant digits.

Evaluate tan(46° 31'). Round answers to 3 decimal places.

Search and Rescue The illustration below shows a search and rescue helicopter with a 29° field of view with a search light. If the search and rescue helicopter is flying at an altitude of 615 feet above sea level, what is the diameter of the circle illuminated on the surface of the water?

Big Augie's Pizza now offers equilateral triangle shaped pizzas. How long must the sides of the pizza be to the nearest inch to equal the size of a round pizza with a 17 inch diameter?

A 26 foot slide leaning against the bottom of a building's window makes a 57° angle with the building. The angle formed with the building with the line of sight from the top of the window to the point on the ground where the slide ends is 39°. How tall is the window? Round to the nearest integer.

Classify the triangle as AAS, SAS, SSA, SAS, or SSS given the following information. c $\gamma$

If sin θ = , and the terminal side of θ lies in quadrant I, find tan θ.

Carousel. A boy wants to jump onto a playground carousel that is spinning at the rate of 15 revolutions per minute. If the carousel is 51 feet in diameter, how fast must the boy run, in feet per second, to match the speed of the carousel and jump on? Round to two decimal places.

State in which quadrant or on what axis the terminal side of a 1431° angle in standard position lies.