This week in math we reviewed our trig understandings of last year, and added some more information that as a collective we can use to solve more advanced questions. This understanding of trig is important because it is fundemental for our future in math and quite often, trig is an understanding that can be very helpful in day to day life. I chose this topic because I am a very visual learner, and being able to sketch and lable my own triangles is very satisfying and important to my general understanding.
Lets take a look at some examples…
Example 1.
Step 1. I am given some information regarding a right angle triangle, but I am not so sure what all of it means so lets take a look. We are told that point (5,8) is on the terminal arm if an angle in standard position.
Point (5,8) means that this point is 5 units right from the vertex (0,0) on the x axis, and 8 units up the y axis.
The terminal arm refers to the arm of an angle in standard position that meets the initial arm at the origin to form an angle.
Finally, standard position means that an angle’s vertex is located at the origin and one arm is on the positive x-axis.
Lets sketch this triangle… we know that the base of the triangle is 5 units long, and it stands 8 units tall.
Step 2. Determine distance from origin (0,0) to P – in other words find the missing side which is the hypotoneuse. To do this we need to use pythagorean theorem. As seen in the image, this means that our hyptoneuse is 
Step 3. Find the angle – it is important to note that finding the hypotoneuse was not necessary in finding our angle, but since this post is to explain each step of completeing a right angle triangle, it is still important.
I can use either TAN, COS, OR SIN to find my angle. As seen in the image, I used Tan to get an angle of 58 degrees.
Example 2.
Point (-7,5) is on the terminal arm of an angle in Quad 2.
Step 1. Draw the triangle – you may notice that this triangle is negative, as it is 7 units to the left from the vertex and 5 units up the y axis.
Step 2. Lable sides – I know the adjacent and the opposite but I am unsure of the hypotenuse. The hypotoneuse is the longest side of a right triangle.
Step 3. For the sake of this example, we are going to find the hypotoneuse using pythagoreum theorum. This gives me my hypotoneuse of 
Step 4. Now we find our angle – In my example I used TAN again, but we can use TAN, COS or SIN. This gives me my angle of 36 degrees.
Step 5. Since my triangle is negative, we want to determine the rotation. The Rotation is measured from the initial side to the terminal side of the angle. Since we roared 180 degrees, we take 180 and subtract our angle of 36 to get our rotation of 144 degrees.