Exam 1: Trigonometry

Use a compass to sketch a quarter of a circle of radius 10 centimeters.Using a protractor, construct an angle of in standard position (see figure).Drop a perpendicular line from the point of intersection of the terminal side of the angle and the arc of the circle.By actual measurement, calculate the coordinates of the point of intersection and use these measurements to approximate the six trigonometric functions of a angle.(Round your answer to two decimal places.) ​ ​

Determine which of the graphs below represents the following function y=|x|sin x ​

Select the graph of the function.(Include two full periods.) ​ ​

In traveling across flat land, you notice a mountain directly in front of you.Its angle of elevation (to the peak) is 3.5°.After you drive miles closer to the mountain, the angle of elevation is 9°.Approximate the height of the mountain.(Round your answer upto one decimal place.) ​ ​

Find the point (x, y) on the unit circle that corresponds to the real number .Use your results to evaluate tan t.

The designers of a water park are creating a new slide and have sketched some preliminary drawings.The length of the ladder is a = 26 feet, and its angle of elevation is 60º (see figure). ​ ​ Find the angle of depression from the top of the slide to the end of the slide at the ground in terms of the horizontal distance d the rider travels. ​

You are holding one of the tethers attached to the top of a giant character balloon in a parade.Before the start of the parade the balloon is upright and the bottom is floating approximately 20 feet above ground level.You are standing approximately a = 100 feet ahead of the balloon (see figure).Round your answer to two decimal places. ​ ​ Find the height h of the balloon if the angle of elevation to the top of the balloon is 35º. ​

Determine whether the function below is even, odd, or neither. ​ ​

Determine whether the function below is even, odd, or neither. ​ ​

Find the value of given trigonometric function.Round your answer to four decimal places. ​ ​

Determine two coterminal angles (one positive and one negative) for θ = -489°.

A granular substance such as sand naturally settles into a cone-shaped pile when poured from a small aperture.Its height depends on the humidity and adhesion between granules.The angle of elevation of a pile, θ, is called the angle of repose.If the height of a pile of sand is 11 feet and its diameter is approximately 34 feet, determine the angle of repose.Round answer to nearest degree.

Determine the exact value of the of the quadrant angle π.

Find the value of given trigonometric function.Round your answer to four decimal places. ​ ​

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode.) ​ Sec 221° ​

Evaluate the expression.Round your result to two decimal places. ​ ​

Use a graphing utility to select the graph of the expression below, making sure to show at least two periods. ​ ​ ​

Find the reference angle , and sketch and in standard position. ​ ​

Evaluate the trigonometric function.Round your answer to four decimal places. ​ ​

An object weighing W pounds is suspended from the ceiling by a steel spring (see figure).The weight is pulled downward (positive direction) from its equilibrium position and released.The resulting motion of the weight is described by the function ​ ​ Where y is the distance (in feet) and t is the time (in seconds). Use a graphing utility to select the graph of the function. ​ ​ ​