You can use a reciprocal trigonometric function to solve a real-world problem.
A restaurant is near the top of a tower. A diner looks down at an object along a line of sight that makes an angle of θ with the tower. The distance in feet of an object from the observer is modeled by the function d = 601 sec θ. How far away are objects sighted at angles of 40° and 70°?
Set your calculator to degree mode. Enter the function and construct a table that gives values of d for various angles of θ.
How can you check that your answers are correct?
Multiply the answers by cos θ. If the answers are correct, then the product is 601.
From the table, the objects are about 785 feet away and 1757 feet away, respectively.
Find each value without using a calculator.
Use a calculator to find each value. Round your answers to the nearest thousandth.