sine and cosine problem

[sbsbsbsbsb]

THe problem says;
Prove: If R is any acute angle, (sin R)^2 + (cos R)^2 = 1. (Hint: From any point on one side of <R, draw a perpendicular to the other side.)

The hints my teacher gave me:
1. drop an altitude
2.Label triangle
3. Label sides
4. Use definition of cosine and sine
5. use pythagorean
6. (cos R)^2 = (b/c)^2= b^2/c^2
(sin R)^2=(a/c)^2=a^2/c^2
c^2/c^2 = a^2 + b^2/ c^2
1= a^2/c^2 + b^2/ c^2
Thing im having trouble with is how to put it in a proof form. :?
Any help just to get me started would be great!

 

[Deleted member 4993]

THe problem says;
Prove: If R is any acute angle, (sin R)^2 + (cos R)^2 = 1. (Hint: From any point on one side of <R, draw a perpendicular to the other side.)

The hints my teacher gave me:
1. drop an altitude
2.Label triangle
3. Label sides
4. Use definition of cosine and sine
5. use pythagorean
6. (cos R)^2 = (b/c)^2= b^2/c^2
(sin R)^2=(a/c)^2=a^2/c^2
c^2/c^2 = a^2 + b^2/ c^2
1= a^2/c^2 + b^2/ c^2
Thing im having trouble with is how to put it in a proof form. :?
Any help just to get me started would be great!

Did you sketch the problem as suggested?

Your proof starts from hint #4.

If you worked through the problem (with the sketch) - tell us how did you use hint #5 ?

 

[sbsbsbsbsb]

I did sketch the problem and copied the given and what to prove. So what would I put as the reason to use the definition of cos and sin? I haven't worked through the problem yet so I haven't used hint #5 yet. I guess the thing I'm having trouble with is how to put sin and cos in a proof. They aren't a very strong area for me anyway so that's probably what's giving me trouble in putting them into a proof.

 

[Deleted member 4993]

I did sketch the problem and copied the given and what to prove. So what would I put as the reason to use the definition of cos and sin?

From the sketch - you will need to claim "something" (like sin (ARB) = AB/AR and cos(ARB) = BR/AR) and reason for that "claim" would be definitions of sine and cosine.


I haven't worked through the problem yet so I haven't used hint #5 yet. I guess the thing I'm having trouble with is how to put sin and cos in a proof. They aren't a very strong area for me anyway so that's probably what's giving me trouble in putting them into a proof.