Proving Sin(squared) theta + Cos(squared) theta = 1: Beginner's Guide

[Propaganda777]

Homework Statement

Prove/Show

Sin(squared) theta + Cos(squared) theta = 1

I'm new to vectors and am having difficulty solving this, any help would be greatly appreciated. Thanks.

 

[learningphysics]

Homework Statement

Prove/Show

Sin(squared) theta + Cos(squared) theta = 1

I'm new to vectors and am having difficulty solving this, any help would be greatly appreciated. Thanks.

There are multiple ways to do this... what are you supposed to start with... is this regarding dot product by any chance?

 

[Proggle]

Remember you can write a unitary vector as:

cos(theta) i + sin(theta) j

Shouldn't be too hard to go from there.

 

[HallsofIvy]

Homework Statement

Prove/Show

Sin(squared) theta + Cos(squared) theta = 1

I'm new to vectors and am having difficulty solving this, any help would be greatly appreciated. Thanks.

This has nothing to do with vectors! It's the Pythagorean theorem!

 

[Propaganda777]

My instructor said solve it any way possible. Could someone show me how to work it out using the pythagorean theorem, I'm still very lost at this.

 

[learningphysics]

My instructor said solve it any way possible. Could someone show me how to work it out using the pythagorean theorem, I'm still very lost at this.

Suppose you have a right triangle with hypoteneuse 1, and an angle theta. What are the lengths of the other two sides?

 

[Propaganda777]

we just learned angle theta today, and as ignorant as this sounds what exactly is an angle theta. I understand where it is on the right triangle, but does it have an exact amount of degrees and how does it relate to the problem in helping to solve it.

 

[Propaganda777]

okay so
Sin theta = y/r and
Cos theta = x/r

correct?

 

[learningphysics]

okay so
Sin theta = y/r and
Cos theta = x/r

correct?

yeah... so y = rsintheta. x = rcostheta

we know that by the pythagorean theorem x^2 + y^2 = r^2. sub in the values of x and y in terms of theta...

 

[Propaganda777]

its been a while since I used the pythagorean theorem so...

x^2+y^2 = 1

now where would I go from here since there are two variable to solve for? lol I'm just forgetting all the basics.

 

[Propaganda777]

If I remember correctly, angles play a role in solving for two variables, right

 

[Propaganda777]

ok I think I got it,

Sin^2 theta = (.71/1)^2
Cos^2 theta = (.71/1) ^2

(.71/1)^2 + (.71/1)^2 = 1.0082 (about 1)

thanks for the help:)

 

[learningphysics]

ok I think I got it,

Sin^2 theta = (.71/1)^2
Cos^2 theta = (.71/1) ^2

(.71/1)^2 + (.71/1)^2 = 1.0082 (about 1)

thanks for the help:)

yeah, but you don't need to assume a particular theta...

x^2 + y^2 = r^2

(rcostheta)^2 + (rsintheta)^2 = r^2

then divide both sides by r^2

and you get

(costheta)^2 + (sintheta)^2 = 1