Assessment # 4

1. What is this problem about?

This problem is from Unit S Concept 7. Concept 7 is about solving equations with half-angle formulas. This video will go over number 3 from the SSS.

2. What does the viewer need to pay attention to in order to do the problem correctly?

The first thing that we need to do is replace the half angle of sine with its half angle formula. There is a radical in the formula, so later in the problem we square both sides to get rid of the radical. When we square both sides we need to remember to check for extraneous solutions. The most important thing about this problem is to check for extraneous solutions because some of the answers we get may be wrong.

Assessment #3

1. What is this problem about?
This is a problem from Unit S Concept 3 Number 1 from the SSS. Concept 3 was about using the power reducing formulas. For this concept, the viewer has to keep in mind that we want the highest power to be one.

2. What does the viewer have to pay attention to in order to do the problem correctly?
The viewer needs to remember that the highest power has to be one, so they need to reduce everything else that is bigger than one. The viewer also needs to follow each step because these problems can get tricky and the process is kind of long.

Assessment #2

I chose to work with the angle 105.

In Unit R, we solved it with the sum and difference formulas

In Unit S, we learned how  to solve it with half angles

In both pictures, the same angles was used in the problems. In the first picture  we solved by using the sum and difference formulas. This means that we used two angles that added up to 105 degrees, in this case the angles were 60 and 45. then we used the ordered pairs from the unit circle and plugged them into the formulas to solve. In Unit S, we learned about half-angles. Basically, we can solve for an angle that is not on the unit circle by using an angle that is on the unit circle and diving it by two. Then we use the ordered pair from the unit circle and plug it into the formulas to solve. We know that these answers are the same because we used the same angle in both of the problems. In one of the pictures, we added two angles to make 105 and in the second picture  we divided an angle by two to get 105. Since we used values from the unit circle, the answers were the same because the ordered pairs on the unit circle are similar to each other. To prove that the answers in both of the pictures are the same, we can plug them into our calculator and compare the decimal answers. 

Unit R Concept 3: Student Problem

The problem that I chose to do is sin(sin^-1(½) + cos^-1(rad. 2/2)

1. What is this problem about?
This problem is from Unit R Concept 3. This concept is about doing the trig of an inverse trig function. To do this we need to use the sum and difference formulas to prove.
2. What does the viewer need to pay close attention to in order to do the problem correctly?
In order to do this problem correctly, we need to choose the correct angles first. If we choose the wrong angles, we will not get the correct answer. Also, in some problems, there will be more than one possible angle choice so we need to make sure that we use the angle in the first quadrant.

Unit R Concept 2: Student Problem

This is the problem that I will solve for Unit R Student Problem 2

This picture shows what we get when we solve for sin(u+v)

This is the work that we need to show when we solve for tan(u-v)

1. What is this problem about?

This problem is from Unit R Concept 2. Concept 2 is about using sum and difference formulas when given values. In this concept we had to use right triangles and Pythagorean Triples to solve. 

2. What does the viewer need to pay close attention to in order to do the problem correctly?

In Concept 2, we had to deal with quadrant 2 and quadrant 3 triangles. For this specific problem, we need to make sure that we draw our triangles in quadrant 2 and that we do not get the signs mixed up. We also need to make sure that sine is positive and that cosine and tangent are negative since it is a quadrant 2 triangle. 

Unit R Concept 1: Student Problem

This is the  problem that I will solve for this student problem.

This is the work for this student problem. This part shows the work using the difference formulas.



































This part of the problem uses the sum formulas to solve.

1. What is this problem about?
This problem is from Unit R Concept 1. Unit R is about sum and difference identities. Concept 1 focuses on finding the exact values of sums or differences. To do this we need to find what the angles add or subtract to.
2. What does the viewer need to pay close attention to in order to do the problem correctly.
First of all the angles that we have is 165. This angle is not on the Unit Circle, but we can use two angles that are on the Unit Circle to solve this problem. In this problem we are going to use 210 and 45 degrees and subtract them in order to get 165. Since we subtracted the angles we need to make sure we use a difference formula to solve this problem.

Unit Q Post # 3

Here are four problems from concept 4 that are worked out:

Level 1:

Level 2:

Level 3: 

Level 4: