Section Objectives
Let be an acute angle of a right triangle. We can define the trigonometric functions at in terms of the lengths of sides of the right triangle.
There are six basic trigonometric functions: sine (), cosine (), tangent (), secant (), cosecant (), and cotangent ().
Trig students often remember the right triangle definitions of the sine, cosine, and tangent by using SOH CAH TOA.
Let be the smallest angle of the 5-12-13 right triangle. Sketch the triangle and find the values of all six trig functions at .
Think back to your geometry class when you studied the -- triangle with legs of length 1. Sketch the triangle and use it to find the values of all six trig functions at .
Think back to your geometry class when you studied the -- triangle with sides of length 1, , and 2. Sketch the triangle and use it to find the values of all six trig functions at and .
Because the acute angles of a right triangle are complementary, it is easy to understand the following cofunction identities.
Trigonometric identities can be extremely useful. Here are a few basic identities that follow immediately from the definitions:
These next identities are called Pythagorean identities.
Show that
Show that
At 19 feet from the base of a flagpole, the angle of elevation to the top is . How tall is the flagpole?
Sketch the unit circle and a 1st quadrant angle, . The sine and cosine of are easily described in terms of the coordinates of the intersection point of the terminal side and the circle. This is unit circle trigonometry.