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Mathematics 20 Online
OpenStudy (anonymous):

solve : 1- sin^2 135

OpenStudy (anonymous):

Isn't there some more info; write down the problem as given.

OpenStudy (anonymous):

Given is equal to Cos^2 135 = Cos^2 (90 + 45) That help?

OpenStudy (anonymous):

no , the question is to choose the correct answer : 1)0 . 2) -1 3)1

OpenStudy (anonymous):

1/2

OpenStudy (anonymous):

please explain how u got 1\2

OpenStudy (anonymous):

\[135\approx \pi/4\]

OpenStudy (anonymous):

\[1-\sin^2135=1-(\sin135)(\sin135)=\]\[1-(0.707...)^2=1/2\]

OpenStudy (anonymous):

without using calculator !!

OpenStudy (anonymous):

Without calculate it is angle pi/4, same thing.

OpenStudy (anonymous):

Given is equal to Cos^2 135 = Cos^2 (180 - 45) = -Cos^2 (45) = 1/2

OpenStudy (anonymous):

1- sin^2 135 = 1- sin^2(3pi/4)=cos^2 (3pi/4)=(1+cos (2*3pi/4))/2=(1+cos(3pi/2))/2=(1+0)/2 = 1/2

OpenStudy (anonymous):

thank you all for your help ...

OpenStudy (anonymous):

you're welcom

OpenStudy (anonymous):

okay. sin 135=sin45. The sine curve is symmetrical about 90 degrees. So you now have a triangle with hypotenuse=1 and two equal side (because the angle is 45 degrees). So:\[1^2=(1/\sqrt{2})^2+(1/\sqrt{2})^2\]So each side is of length \[1/\sqrt{2}\]Thus the sine of the angle is \[\sin 135=\sin 45=(1/\sqrt{2})/1=1/\sqrt{2}\]and \[1-\sin^2135=1-(1/\sqrt{2})^2=1/2\]

OpenStudy (anonymous):

If you use Cos^2 + Sin^2 = 1 and Cos (pi-t) = - Cos t, the answer follows.

OpenStudy (anonymous):

sorry , in fact the question is 1-2 sin^2 135 . so i didn't write 1\2 in the choose but i got the idea , thanks

OpenStudy (anonymous):

lol. then answer is 0

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