Student Problems

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Student Problem #8: Unit R. Concept 1

Sum Formula:

*What is the purpose of this picture?

This picture demonstrates the use of the sum formulas for sine, cosine, and tangent being put to use to find exact values for these trigonometric functions.

*What should you pay close attention to in order to understand the concept?

Understand that 450* is not a normal angle from the unit circle. Here, I have added two values FROM the Unit Circle [of the normal reference angles to 30*, 45*, 60*, 90*, etc.,] that amount to 450*, those being 300* and 150*. (* = degrees symbol)

Difference Formula:

*What is the purpose of this picture?

This picture depicts the use of the difference formulas for sine, cosine, and tangent being put to use to find exact values for these trigonometric functions.

*What should you pay close attention to in order to understand the concept?

Due to the fact the 450* is going on to a second revolution of the Unit Circle, I have to use 720* because its a large value and can subtract another value (270*) to make 450*.  >>>NOTE: 720* is exactly two entire revolutions of the Unit Circle and its reference angle is 360* thus the ordered pair is the same. 

***CHECK: check if you are correct by plugging in the sin(450), cos(450), and tan(450) into your calculator. 

>>>NOTE: because sine is 1, cosine is 0, and tangent is undefined, what does that tell you about this angle???

         ***It is a quadrant angle!!! The reference angle of 450* is 90* :)

Hope this helped! If you need any clarification or for me to further describe verbally leave a comment down below. If you would prefer a video instead, also leave a comment. :)

Student Problem #9: Unit R. Concept 2

What is this problem about?

This photograph shows how to the sum and difference formulas (look at Unit R. Concept 1 for reference) are integrated in the use of solving for right triangles.

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

Be aware that these triangles do lie in different quadrants! Because of this, the problem is still solved the same way as you normally would if both triangles were in the same quadrants, however, note whether sin, cosecant, cosine, secant, tangent, or cotangent are positive or negative [this depends on which quadrant we refer to.]  Please note that triangle drawn on the left is the 'u' and the triangle drawn on the right is the 'v' [my penmanship wasn't all that great here]. Be sure that you chose the correct formula for what is being asked. I can't stress that enough. If you use the wrong formula, evidently you will get the wrong answer!

Student Problem #10: Unit R. Concept 3

*What is this problem about?

This problem in particular depicts how to use the sum formula in solving the trig of an inverse trig functions. Although this may sound big and scary, it really is NOT! As you can see from the above problem, the inverse trigonometric function is inside the brackets (thats the inverse trig part if that wasn't obvious enough.) The regular trig part is what is outside the problem. Now that you can distinguish each part, it doesn't sound so scary now, right? 

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

Please understand that the way I got my coordinate pairs was through my referencing the Unit Circle. Yes, the Unit Circle is being used again! Moreover, for tangent, I realize that I could have used the ordered pair of (-1,0) as well because 0/-1 is also 0, however, I don't need to. I am picking the values closest to quadrant I. This has absolutely nothing to do with some sort of mathematical process, its just the way we solve these kinds of problems for my Math Analysis class, however, feel free to solve using that as well. :)