Trigonometric Functions

1. OPEN ENDED Draw and label an example of an angle with negative measure in standard position. Then find an angle with positive measure that is coterminal with this angle.
2. Writing in Math Use the information on page 779 to explain how trigonometry is used in building construction. Include an explanation as to why the ratio of vertical rise to horizontal run on an entrance ramp is the tangent of the angle the ramp makes with the horizontal.
3. Writing in Math Use the information on page 796 to explain how you can model the position of riders on a skycoaster.

High
M
GET READY for the Lesson
1 ft
The Americans with Disabilities
Act (ADA) provides regulations
designed to make public buildings
accessible to all. Under this act,
the slope of an entrance ramp
designed for those with mobility
angle
A
disabilities must not exceed a ratio
of 1 to 12. This means that for
every 12 units of horizontal run,
the ramp can rise or fall no more than 1 unit.
When viewed from the side, a ramp forms a right triangle. The slope
of the ramp can be described by the tangent of the angle the ramp
makes with the ground. In this example, the tangent of angle A is 12
1211
B
Trigonometric Values The tangent of an angle
is one of the ratios used in trigonometry.
Trigonometry is the study of the relationships
among the angles and sides of a right triangle.
hypotenuse
op
leg
Consider right triangle ABC in which the
measure of acute angle A is identified by the
Greek letter theta, 8. The sides of the triangle
are the hypotenuse, the leg opposite 0, and the
leg adjacent to e
A
adjacent leg
Using these sides, you can define six trigonometric functions: sine,
cosine, tangent, cosecant, secant, and cotangent. These functions are
abbreviated sin, cos, tan, csc, sec, and cot, respectively.
KEY CONCEPT
Trigonometric functions
If e is the measure of an acute angle of a right triangle, opp is the measure
of the leg opposite e, adj is the measure of the leg adjacent to e, and hyp is
the measure of the hypotenuse, then the following are true.
OPP
adj
OPP