Question

0= cos^2 theta - sin ^2 theta

how do i know whether i should switch cos^2 theta to (1-sin^2 theta) or switch sin^2 theta to ( 1- cos^2 theta)
both ways work but give a different answer

Answer 1

im guessing this is for integral of sin/cos -- ( it all depends wat u get, sometime it will cost more work if u used the other one)

Answer 2

sin^2(theta)=cos^2(theta) implies tan^2(theta)=1 implies tan(theta)= +-1 implies theta = arctan(+-1) implies theta = +- pi/4, which you can see is a solution upon inspection.

Answer 3

Technically there are infinite answers, but this is two of them.

Answer 4

I was thinking..\[cos^2 \theta - sin ^2 \theta = cos2\theta\]

Answer 5

i need to solve for theta..i dont think cos2theta will have the answer of 45deg

Answer 6

but technically, all ways should work out isnt it..i dont understand why it gives different answers ..so how do i know when to use what

Answer 7

@iHelp but both ways give different answers...so is not more work..or did i do something wrong..

Answer 8

I did solve for theta...why does no one see that?

Answer 9

because dont really understand what u said..

Answer 10

Actually... All the above method gives you the answer 45 ...

Answer 11

And 45 is an answer because cos(45)=sqrt(2)/2=sin(45) implies sin^2(45)-cos^2(45)=0
Which is your equation...

Answer 12

So I'm right...

Answer 13

how is sin theta = cos theta...
yea.. the answer is 45deg
but i want to know why when i do
0 = cos^2 theta - （ 1- cos^2 theta)
it doesnt give 45 as the answer

Answer 14

cuz sin^2 theta + cos^2 theta = 1
sin^2 theta = 1 - cos^2 theta

so my equation should work out too

Answer 15

Method I:\[cos^2\theta-sin^2\theta =0\]\[1-sin^2\theta-sin^2\theta =0\]\[1-2sin^2\theta =0\]\[sin^2\theta =1/2\]\[sin\theta =\sqrt{1/2}\]\[\theta =45\]

Answer 16

Method II
\[cos^2\theta-sin^2\theta =0\]\[cosn^2\theta-(1-cos^2\theta) =0\]\[2cos^2\theta -1=0\]\[cos^2\theta =1/2\]\[cos\theta =\sqrt{1/2}\]\[\theta =45\]

Answer 17

ohh...i find the angle using 1/2 first and then divide it by 2, i caught my mistake thanks!

Answer 18

Method III:
\[cos^2\theta-sin^2\theta =0\]\[cos2\theta =0\]\[2\theta =90\]\[\theta =45\]

Answer 19

wow thanks so much. my doubts are clear (:

Answer 20

Yay~ Glad to hear :)

Answer 21

As you see, method III is the fastest :P just kidding :)