Right Triangle Trigonometry

Consider a right triangle, with one of the acute angles labeled as θ, as shown below. Relative to θ, the 3 sides of the triangle are the hypotenuse, the opposite side, and the adjacent side.

  

6 ratios can be formed from this triangle that define the 6 trigonometric functions of the angle θ.

Sine            Cosine            Tangent            Cosecant            Secant            Cotangent

 Note: 0º < θ < 90º and the value of each trigonometric function is positive

         

         

Look! The functions in the second row, are the reciprocals of the functions above them! 

Hint!     SOH            CAH            TOA             CHO            SHA            CAO

Evaluating Trigonometric Functions

Find the 6 trigonometric functions of θ.

 

Find the value of a.

Sketch a right triangle corresponding to the trigonometric function of θ. Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of θ.

                                       

                                       

Other math help sources:

-http://www.regentsprep.org/Regents/math/ALGEBRA/AT2/Ltrig.htm
-http://www.themathpage.com/atrig/solve-right-triangles.htm
-http://www.uiowa.edu/~examserv/mathmatters/tutorial_quiz/trigonometry/righttriangletrig.html
-The textbook
-Mr. Wilhelm!