Unit S:Assessment 4

1. What is this video about?
This video is about simplifying the equation in which there will be factors that allows you to use Zero Product Property method to find the degree/radian values.
2. What must the reader pay close attention to in order not to make a mistake? 
Readers must pay attention on how to get LCD(least common denominator) and when you do, you must multiply the numerator and denominator by the same thing. Readers also must know how to use Pythagorean identities and how to re-arrange them because that will make substitution much easier.

Unit S: Assessment 3

1. What is this video about?

This video is about reducing a certain equation/expression to a point in which the highest power at the end is 1. For example: if we have tan^2(x), we would want to simplify that expression to something to the first power and get rid of the square on the tan function somehow.

2. What must the reader pay close attention to in order not to make a mistake? 
The majority of this problem is made up of just simplifying and plugging in. Anytime we are working with a lot of plugging in and simplify, we would want to substitute in those large variables and coefficients with a different variable such as y so we don't get confused when plugging in values into a formula. Readers also need to make sure to multiply out the coefficients when substituting back in or that will mess up your answer in the end.

Unit S: Assessment 2

The methods used in both of these pictures(sum/difference and half angles) are used to find the value of angles that are not memorized or on the unit circle. Even though both methods differ in technique, both ended up with the same answers and I know these answers are the same because when i plug both methods into the calculator, I received the same answers for sin,cos, and tan. You should get the answer for both because the main purpose of these two methods are to find the value of a certain angle.

Student Problem #3

1) What is this problem about?
This problem is about solving the trig of an inverse trig function and finding the value of the sum and difference formula without a calculator.

2) What must the reader pay close attention to in order not to make a mistake? 
Readers need to pay close attention that to convert pi/6 to 30°, you have to multiply it by 180/pi and then reduce. Readers also need to pay attention what the coordinate values of a 30° angle is and how to find the missing side of a triangle when we only know two values. Readers also need to know what quadrant(s) the triangle is in because that will determine the number of answers you will receive in the end.

Student Problem #2

1) What is this problem about?
This problem is about using the sum and difference formulas when given values for a right triangle. We are given the values of the trig functions but we must be able to label it correctly on a triangle depending on which quadrant it is located in.


2) What must the reader pay close attention to in order not to make a mistake? 
Reader must pay close attention to what quadrant the triangle is in. Sometimes we are given 2 trig functions and the answer in the end would contain two different answers but lucky for us, we know all three values and know what quadrant the triangle is in. Readers also must pay close attention to the type of signs used depending on what sum and difference formula we are using. Remember that you can only add and subtract with common denominators as seen in the numerator part of the tan difference formula.

Student Problem #1

1) What is this problem about?
This problem requires us to be able to find the exact values for the following trig functions and must learn to correctly choose an angle to works for all three equations









2)What must the reader pay close attention to in order not to make a mistake? 
Readers must pay close attention to the fact that there are a large list of angles to choose from and they don't have to be restricted to using only one pair. Readers also must be careful with denominators when adding and subtracting because you can only add and subtract when there is a common denominator. 

Concept 4 Problems

Step1 : set cot(x)= to its ratio which is x/y. 
Step2: Find the reference angle that makes the equation equal to 1. So the only one that works is 45°.
Step3:Determine the quadrants we will have our answers in. Since cot(x)= positive answer the x and y values must both be either positive or negative. So the quadrants that work for that is 1st and 3rd.
Step4:To find the angle in quadrant1, we just use the RA which was 45° and to find the angle in the third, take the RA and add it to 180° which makes it 225°.
Step5:Convert our degree answers to radians by multiplying 45° and 225° by pi/180°.

Step1:Isolate the csc(x) by dividing both sides by √3 and then rationalize toget csc(x)=2√3/3. 
Step2 : set cot(x)= to its ratio which is x/y. 
Step3: Find the reference angle that makes the equation equal to 2√3/3. So the only one that works is 60°. Since r=1 and dividing by a fraction is the same thing as multiplying by its recip.
Step4:Determine the quadrants we will have our answers in. Since csc(x)= positive answer, the  y values must positive. So the quadrants that work for that is 1st and 2nd.
Step5:To find the angle in quadrant1, we just use the RA which was 60° and to find the angle in the second, take the RA and subtract it from 180° which makes it 120°.
Step6:Convert our degree answers to radians by multiplying 60° and 180° by pi/180°.

Step1:The problem we are looking at looks similar to a quadratic equation so we can substitute sin(x) for u. After factoring it out, plug back in the sin(x) for all u-variables.
Step2 : Now we want to use Zero Product Property and set sin(x)= to its ratio which is y/r and make it equal to 0.
Step3: After solving for the ratio values, we see that y=0 and -1. 
Step4:Determine the quadrants we will have our answers in. Since y=0 and -1, then we are looking at quadrant angles and those angles are 0°,360°,180°, and 270°.
Step5:Convert our degree answers to radians by multiplying 0°,360°,180°, and 270° by pi/180°.

Step1:We don't want to work with the 2x attached to the cos yet so we are going to sub it out for the variable(u).
Step2 : set cos(x)= to its ratio which is x/r. 

Step3: Find the reference angle that makes the equation equal to -√3/2. So the only one that works is 30°.
Step4:Determine the quadrants we will have our answers in. Since cos(u)= negative answer, then the x-value must be a negative. So the quadrants that work for that is 2nd and 3rd.
Step5:To find the angle in quadrant2, we just take the RA and subtract it from 180° which makes it 150°. and to find the angle in the third, take the RA and add it to 180° which makes it 210°.
Step6:Since u=150° and 210°, plug back in the 2x for the u variable and solve for the unknown variable, so our final answers should be 75° and 105°.