Exam 1: The Six Trigonometric Functions

An airplane is approaching Los Angeles International Airport at an altitude of 10,560 feet. If the horizontal distance from the plane to the runway is 2.1 miles, use the Pythagorean Theorem to find the diagonal distance from the plane to the runway (see the figure below). (5,280 feet equals 1 mile.) a = 2.1 miles, b = 10,560 feet

Find sec  θ  if  and θ  terminates in QIII. ​

Show that the following statement is true by transforming the left side into the right side.

Find an angle θ  in the second quadrant for which cot  θ = - 1. Look for an angle between 0° and 360°. __________

Multiply. ​

Add or subtract as indicated. Then simplify your answer if possible. Leave the answer in terms of sin  θ  and/or cos ​ θ .

Find the right part of the identity. __________ ​

Find A  if B = 20° and  α +  β = 120°. Remember: The sum of the three angles in any triangle is always 180°.

Give the reciprocal of the given number. ​

Find all six trigonometric functions of θ  if the given point is on the terminal side of θ . ​

Draw the following angle in standard position; find the sine, the cosine, and the tangent of the angle below. ​

Add or subtract as indicated. Then simplify your answer if possible. Leave the answer in terms of sin  θ  and/or cos  θ . ​

Give the reciprocal of the given number.

Draw the following angle in standard position and then name the reference angle. ​

Add or subtract as indicated. Then simplify your answer if possible. Leave the answer in terms of sin  θ  and/or cos  θ .

For this problem, recall that  means . If  find . Simplify the answer. Do not convert to decimal form.

An isosceles triangle is a triangle in which two sides are equal in length. The angle between the two equal sides is called the vertex angle, while the other two angles are called the base angles. If the vertex angle is 40°, what is the measure of the base angles? __________°

Find the remaining sides of a 45° - 45° - 90° triangle if the longest side is 20.

An escalator in a department store is to carry people a vertical distance of 19 feet between floors. How long is the escalator if it makes an angle of 30ᵒ with the ground? __________ feet.

Suppose the angle formed by the line y = 8 x and the positive x -axis is θ . Find the tangent of θ . tangent of θ =  __________