Assessment #2: Unit S Concept 4

Solving exact value of an angle using

Half-angle
formulas

Solving exact values of an angle using the

Sum formula!

How do we know these are both the same answers?? 

We know that the answers from both pictures are the same because we can check it by plugging it correctly into a calculator. By plugging it in and then plugging in the sin, cos, and tan of 75° we can see that they are the exact same answer. In fact, the tangent of 75° for both the sum and difference formulas and the half-angle formulas gave us the exact same value for both. The sin of both answers plugged in the calculator gives us a value of .9659258....... The cosine gives us a value of .258819.......... The tangent gives us a value of 3.73205...... You can even try it in your calculator to see that these values are what you get if you plug in those crazy radical answers from above.