Speedy Gonzalez Math

Tuesday, April 16, 2013

Student Video Concept 7 #3

This video explains step by step how to solve an equation with half angle formulas. The problem that we will solve is sin(x/2)+cos(x)-1=0. When solving this problem you need to make sure to check for extraneous solutions. Because we squared both sides, we may have created answers that are not really solutions to the problem. To check for extraneous solutions, plug your answer values back into the original formula, and check if the answer is true.

Monday, April 15, 2013

Student Video Concept 3 #5

This video explains how to use power reducing formulas to reduce our problem so that the problem has the highest power of 1. The problem that we will be reducing is sin^2(x)cos^2(x). Pay close attention when foiling that (2x) is a variable and does not get foiled. Also, pay attention to when we substitute (m) for 2x and know that you will have to plug 2x back in for the value of m. Lastly, you may have to use the power reducing formulas more than once to reduce everything down to the highest power of 1.

Sum and Difference formula in relation to the half angle formula

The first picture depicts using the half angle formula to find the sine,cosine,and tangent for the angle 105 degrees. The second picture shows using the sum formula to find sine,cosine, and tangent for the same angle. When using the half angle formula, you need to pay attention to what is positive and negative based on the quadrant that your half angle is in. When we solve with the half angle formula and the sum formula we find that our answers are the same for sine, cosine, and tangent. Our answers are written differently when we solve using both formulas, however they are equivalent. We can check by plugging in our answers for sine,cosine,and tangent for both formulas in our calculator , and we find that our answers are the same. The two pictures above depict how to plug our answers into our calculator and shows that they are the same.