During this semester we began learning a formula called Pythagorean Theorem, a2+b2=c2, we did so by completing worksheets such as Proof by Rugs. We started by taking a rectangle and then splitting the rectangle into right triangles, we were then able to find the lengths a, b, and c. After that we were able to use the distance formula, √(x2−x1)2+(y2−y1), from Pythagorean Theorem and then went on to construct right triangles. After that we used the distance formula to obtain the equation of a circle in the center at the origin of the Cartesian coordinate plane. This was done by finding the distance between the points on a coordinate plane like (4, 3) and (-1, 2). The next step was to take the given points and then plug it into x2+y2=4 which happens to be a circle with a radius of 2 which was given and then solving for the distance between.
The unit circle is a circle with a radius of 1 and does have some points that end up being square roots and other being fractions. After that we had to find the points on the unit circle, at 30, 45, and 60 degrees, this was solved by plugging numbers in x2+y2=1. The next step was to use the symmetry of a circle to find the remaining on the unit circle. To do this we used our existing knowledge on the Cartesian coordinate plane and apply what we learned about the quadrants to all the points that were to be filled out. And when that step was completed our next task was to use the unit circle to define sine and cosine. To do this we first took a triangle in the until circle and then attempt to find one of two lengths in the 3 sided triangle using the angles given. To solve the triangle all we had to do was use sine and cosine.
Then we began to learn about the tangent function which I will insert my notes on how I learned how to do it. Once we got the hang of that we then had to use similarity and proportions to obtain sine, cosine and tangent. This able to be done by working on Right Triangle Trig: Find the Missing Side lengths which we used sine, cosine and tangent to complete the sheet. And after that our next task was to use the unit circle to define arcSine, arcCosine and arcTangent functions. The next step was to use the Mount Everest problem to learn more about the Law of Sines and how it would be used in this problem.
The final steps that we did was work on a worksheet called Trigonometry Law Practice where we were given info from a triangle and then went on to solve the law of sines and cosines. And then also how to derive the law of sines and cosines
The unit circle is a circle with a radius of 1 and does have some points that end up being square roots and other being fractions. After that we had to find the points on the unit circle, at 30, 45, and 60 degrees, this was solved by plugging numbers in x2+y2=1. The next step was to use the symmetry of a circle to find the remaining on the unit circle. To do this we used our existing knowledge on the Cartesian coordinate plane and apply what we learned about the quadrants to all the points that were to be filled out. And when that step was completed our next task was to use the unit circle to define sine and cosine. To do this we first took a triangle in the until circle and then attempt to find one of two lengths in the 3 sided triangle using the angles given. To solve the triangle all we had to do was use sine and cosine.
Then we began to learn about the tangent function which I will insert my notes on how I learned how to do it. Once we got the hang of that we then had to use similarity and proportions to obtain sine, cosine and tangent. This able to be done by working on Right Triangle Trig: Find the Missing Side lengths which we used sine, cosine and tangent to complete the sheet. And after that our next task was to use the unit circle to define arcSine, arcCosine and arcTangent functions. The next step was to use the Mount Everest problem to learn more about the Law of Sines and how it would be used in this problem.
The final steps that we did was work on a worksheet called Trigonometry Law Practice where we were given info from a triangle and then went on to solve the law of sines and cosines. And then also how to derive the law of sines and cosines