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Sin cos tan of exterior right triangle
Posted by Tommy on June 18, 2024 at 7:03 pmI am studying for the FS exam and am having trouble with these trig problems. The FS handbook doesn’t give an explanation on how these are solved and I can’t seem to find much about exterior angles online. First pic is of questions #1 and 2, second pic is of the answers.
OleManRiver replied 2 months, 3 weeks ago 7 Members · 9 Replies 
9 Replies

Sort of a trick question; the answer is the same as the acute angle that you’re looking at.

If you have a good math text covering trigonometry to work from, you would be looking for the idea of trig ratios for angles greater than 90 degrees. In the index, you might look for “related acute angle” or “principle angle”.
Those concepts from trigonometry should explain the reason BStrand points out that the acute angle is the key.

That is a really welldesigned problem. The figure is drawn on an xy plane with the hypotenuse originating at the origin. BStrand is spot on.
Note that in problem 2, the length along the xaxis is negative, so any trig function involving that side is going to be negative. That would be the tangent, the cotangent, the cosine and the secant. The tangent is 9/(12) (opp over adj) and the others follow.
In problem 3, both the x and y lengths are negative, so the tangent and cotangent will be positive, the sine and cosecant negative, and the cosine and secant negative.
As you study review the Unit Circle where the derivations for angles greater than 90 degrees are usually discussed. The angle you are looking to evaluate is always the angle made by the hypotenuse and the xaxis. The functions themselves are then the sohcahtoa definitions.
Also note that the triangles are both similar to 345 triangles, so the answers are going to reduce to thirds, fourths, and fifths.
Good luck and thanks for sharing the problems.

@mathteacher I am sorry maybe it’s the muscle relaxers but I am feeling a bit juvenile. Sin = Oscar has cos = a harry tanj = old a$$. . That’s is how a poor redneck learned it lol. There was one about a hippy on acid or something as well. One of those things that a teacher who was doing his best not to beat my teenage head in while tutoring me to get these things memorized. He found a way. Great teacher and that was the only bad word I had ever heard him say. He said it took me to break his record lol.

I had a chemistry teacher do something like that in highschool. Au (Eh you, give me that gold) and Ag (Ah gee, it’s only silver).

I never used those memory aids when I was a student and only learned about them when I started teaching at age 56.
My colleagues had one to remember the signs of the functions in different quadrants: Appalachian State Teachers College. All functions are positive in the first quadrant, only the Sine in the second quadrant, only the Tangent in the third quadrant, and only the Cosine in the fourth quadrant. Now Appalachian State Teachers College became Appalachian State University long ago, but math education being what it is, the memory aid persisted.
So, I updated it to Alcoholic Students Talk Continuously. My students loved it, my colleagues hated it and I guess it was further evidence that I should never have been allowed to teach teenagers.
Whatever.

Being an electrical engineer, and since the angle is being measured from (0, 0), I think of a graph of the sine and cosine functions. These are smooth everywhere, with no sudden jumps when the angle goes from acute to obtuse, and at the other quadrant changes as well. That’s enough for me to confirm the magnitude of the sine and cosine will be the same for the interior or exterior angle. From the position on the graph of sine and cosine, I can find the sign. As for cowhatever, I’d have to look those up; I never used them in my professional life. I don’t think I even used them in college, just high school.

Like they said, but I don’t do memory aids either. The sin of an angle is the same as the sin of its compliment, so in your first example the sin there is still = a/c, upright/hypotenuse or however you want to imagine a right triangle
dd 
Hey it’s teachers like you that made something that was extremely difficult for a dyslexic person to see the fun and understanding that math and other subjects could be. I understand not everything has to be fun. But even as a Jar Head I had fun when it was cold and raining humping a pack in mud. I try and always look at the positives and try and have fun doing whatever it is. Enjoying life and such.
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