Use of trigonometric functions:

Given a problem APPLIES the trigonometric functions to solve for the unknown.

As display in the previous lesson the lengths of the sides of right triangles can be solved by using the Pythagorean Theorem.  We know that if the lengths of two sides are known by us then the length of the third side can then be determined using the Pythagorean Theorem.  One real fact about triangles is that the sum of the three angles equals 180°.  If right triangles have one 90° angle, then the sum of the other two angles must equivalent 90°.  Understanding this, we can solve for the unknown angles if we know the length of two sides of a right triangle.  This can be completed through using the six trigonometric functions.

In right triangles, the two sides (other than the hypotenuse) are referred to as the opposite and adjacent sides.     In Figure, side a is the opposite side of the angle and side b is the adjacent side of the angle. The terms hypotenuse, opposite side, and adjacent side are used to distinguish the relationship among an acute angle of a right triangle and its sides.  This relationship is providing through the six trigonometric functions listed below:

Figure: Right Triangle

Sine Θ = a/c = opposite/hypotenuse

Cosine Θ = b/c = adjacent/ hypotenuse

Tangent Θ =a/b = opposite/adjacent

Cosecant Θ =c/b = hypotenuse/ opposite

Secant Θ = c/a = hypotenuse/adjacent

Cotangent Θ = b/a = adjacent/opposite

The trigonometric value for any angle can be determined simply along with the aid of a calculator.  To find out the sine, cosine, or tangent of any angle, enter the value of the angle into the calculator & press the desired function.  Remember that the secant, cosecant, and cotangent are the mathematical inverse of the sine, cosine & tangent, correspondingly. Thus, to determine the secant, cotangent, or cosecant, first press the COS, SIN, or TAN key, then press the INV key.