My first Proof Tell me what you think please

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The discussion centers on the proof of the identity sin(90-theta) = cos(theta) and related trigonometric functions. A participant points out a mistake in the original proof regarding the labeling of a fraction, suggesting it should be GR/OR instead of GR/OM. Additionally, it is recommended to demonstrate the congruence of triangles OSR and OGR to strengthen the proof, using the angle-side-angle (ASA) criterion. After correcting the fraction, the proof is deemed acceptable. The conversation emphasizes the importance of accuracy in mathematical proofs.
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Proving... sin(90-theta) = cos(theta)
along with tan.. cot.. and sec.. csc...
short proof... please let me know if it is correct... thank you.
 

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I see one mistake. You have sin(90 - theta) = GR/OM. That fraction should be GR/OR, according to your drawing.
 
Sorry... that's what I ment to say... but besides that... is it ok?
 
Yeah. Fix that and you should be good.

In case your instructor is very picky, you can show that OS = GR by showing that the triangles OSR and OGR are congruent. Both are right triangles, and angle SOR = angle GRO. Also, angle GOR = angle ORS. Since two angles and the included side of one triangle are congruent to the corresponding two angles and included side of the other triangle, the two triangles are congruent. (ASA - short for angle-side-angle)
 
thnks
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
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