[Trig] Double-Angle and Half-Angle

Luizzmp

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I'm having a lot of problems with questions that involve double angles and half angles... Can someone help me understand how to solve two types of problems?

The first one is: ~Use the following information to find sin 2A, cos 2A, and tan 2A. cos A = 5/13, in quadrant 4.~



The second one is: ~Use the following information to find cos A/2, sin A/2, and tan A/2. There is a right triangle and the leg opposite angle A is 8 and the adjacent leg to angle A is 15.~


There are a lot of questions like these two in my homework. Can someone please tell me how to do them? I have all the formulas in my text book, but I still don't understand how to do it.
 
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stapel

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Use the following information to find sin 2A, cos 2A, and tan 2A. cos A = 5/13, in quadrant 4.
Apply double-angle formulas.


Use the following information to find cos A/2, sin A/2, and tan A/2. There is a right triangle and the leg opposite angle A is 8 and the adjacent leg to angle A is 15.
Use the Pythagorean Theorem to find the length of the remaining side. Find the sine, cosine, and tangent of the angle. Then apply half-angle formulas. ;)
 

Luizzmp

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Apply double-angle formulas.



Use the Pythagorean Theorem to find the length of the remaining side. Find the sine, cosine, and tangent of the angle. Then apply half-angle formulas. ;)

Can you show me where to apply the formulas though? At least for the sin in both problems and I'll figure out how to do it for cos and tan ;)

Yeah. Thats what I did first for the second problem. The Hypotenuse of the triangle is 17, so sin A= 8/17, cos A= 15/17, and tan A= 8/15... but then again, I don't know how to apply the formulas there xD :lol:
 

Subhotosh Khan

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I'm having a lot of problems with questions that involve double angles and half angles... Can someone help me understand how to solve two types of problems?

The first one is: ~Use the following information to find sin 2A, cos 2A, and tan 2A. cos A = 5/13, in quadrant 4.~

If cos(A) = 5/13 → sin(A) = -12/13 → sin(2A) = 2 * sin(A) * cos(A) = ???



The second one is: ~Use the following information to find cos A/2, sin A/2, and tan A/2. There is a right triangle and the leg opposite angle A is 8 and the adjacent leg to angle A is 15.~


There are a lot of questions like these two in my homework. Can someone please tell me how to do them? I have all the formulas in my text book, but I still don't understand how to do it.
.
 

Luizzmp

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If cos(A) = 5/13 → sin(A) = -12/13 → sin(2A) = 2 * sin(A) * cos(A) = ???.

ohhh ._. I think I get it now. Thank you Subhotosh :D I'll try to do the other ones with double angles now...

Is there any chance you could show me how to do one with half angles too? ;)
 
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Subhotosh Khan

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ohhh ._. I think I get it now. Thank you Subhotosh :D I'll try to do the other ones with double angles now...

Is there any chance you could show me how to do one with half angles too? ;)
Do you know the half-angle formulae? What are those?
 

Luizzmp

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Do you know the half-angle formulae? What are those?
I don't remember xD but I am finished with that homework 8) I figured out how to do it with a pm someone from the forum sent me with an example ;3
 
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