(Unit S. Concept 4.) Half Angles Formula and it's similarity with (Unit R. Concept 1) Sum Formula

Solving the Sine, Cosine, & Tangent of 75* with Half Angle Formula

• What does this picture show?

          This picture demonstrates how to solve for a half angle using the Half Angle Formula. Although this looks difficult and challenging, it really isn't--it is just plugging in and using simple algebraic skills to solve. Please understand that this is only one of the methods used to solve for the sin(75), cos(75), and tan(75); one of the other method is demonstrated in the picture below. I have done this problem step-by-step so that it is evident how to use the Half Angle Formula in relation to half angles of the Unit Circle.

• What does the views need to pay attention to in order to understand the problem?

             The quadrant in which we determine whether sine and cosine will be a positive or negative value is dependent upon the 'u/2' NOT the 'u'. The 'u' value is twice as much as the 'u/2' value. In this case twice of 75* is 150*. Although 75* is not apart of the major angle values of the Unit Circle, 150* is. The cosine and sine used in this problem come from the ordered pair for 150*. Knowing these key parts of information along with the Half Angle Formula allow us to solve for the trig function values of half angles like 75* as shown in this example.

Solving the Sine, Cosine, & Tangent of 75* with Sum Formula

• After having solved for the sin(75), cos(75), and tan(75) using these methods, how do you know that the answers are the same?

         Without even plugging anything into your calculator, you automatically know that although the answers look different between the sin(75), cos(75), and tan(75) because different methods were used, they are same. This is because the sin(75) can only be the sin(75), cos(75) can only be equal to cos(75), and tan(75) can only be the same as tan(75). This sounds very obvious, but many people assume that because the way the answers appear are different from one another that the they are different values, but they are not. Once plugged into your calculator, you will see for yourself that the approximate answers for all of them are the same. This is what the picture below shows.