Tangent and Right Triangle

orecchionebruno

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Jun 4, 2018
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Hello, I hope it's not a stupid question but I would have an explanation (please be simple I'm not good in Math
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),

In following picture (from wikipedia) is shown a Right Triangle and it's visible Sin, Cosin and Tangent segments of the angle on the Origin:
trig.jpg

In this 2nd picture (took somewhere), it's shown a right triangle where Tangent is the Hipotenuse, and Sine is Cathetus and Cosine is the other Cathetus:
right_trig.jpg

Considering the Sine, Cosine and Tangent formulas, can you please explain me in 1st drawing how must draw the 2nd right rectangle?

Maybe following drawing that I've done explain it?
I haven't inverted Sine and Cosine, should I do it?

right_trig2.jpg

Thanks in advance
 
Not sure I understand your question. What do you want to draw?
Regarding the first diagram. Let's consider sin(). To understand what's going on note that we have a circle with radius 1. Sin = opposite/hypotenuse. Since hypotenuse is 1 (it's the radius), sin = opposite/1 = opposite, as shown in the diagram.
 
Not sure I understand your question. What do you want to draw?
Regarding the first diagram. Let's consider sin(). To understand what's going on note that we have a circle with radius 1. Sin = opposite/hypotenuse. Since hypotenuse is 1 (it's the radius), sin = opposite/1 = opposite, as shown in the diagram.

Hi lev888

thank you for your answer. The formuala that you applyed is clear and in effect it's correct in according with 1st diagram.

What I would like to understand (may be I'm doing a stupid question), it's considering the Tangent formula.

tan(alfa)=opposite/adjacent where hypotenuse=adjacent*tan(alfa)
How can I draw the formula tan(alfa)=opposite/adjacent if a tangent is a Segment that is outside a Circle?




 
How can I draw the formula tan(alfa)=opposite/adjacent if a tangent is a Segment that is outside a Circle?

It doesn't matter whether 'tangent' is inside or outside the circle. The 'adjacent' segment is the radius, so its length is 1. tan(alfa) = opposite/1 = opposite (blue line).

 
It doesn't matter whether 'tangent' is inside or outside the circle. The 'adjacent' segment is the radius, so its length is 1. tan(alfa) = opposite/1 = opposite (blue line).


Thank you, for your answer, your answer is clear and I'll back to a book to study Tangent. :D

Cheers
 
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