how do i find tan 67.5 with the tangant half angle formula???

Question

asnaseer · Answer

what is 2 times 67.5?

anonymous · Answer

135

anonymous · Answer

Half-Angle formulas sin s/2=+-sqrt((1-cos s)/2), (note:+ or - answer depends on value of sin s/2 not sin s.) cos s/2=+-sqrt((1+cos s)/2), (note:+ or - answer depends on value of cos s/2 not cos s.) tan s/2=sin s/(1+cos s) .. sin 67.5=sin 135/2=sqrt((1-cos 135)/2) =sqrt((1+√2/2)/2)=sqrt((2+√2)/4) =sqrt(2+√2)/2 .. cos 67.5=cos 135/2=sqrt((1+cos 135)/2 =sqrt((1+(-√2/2))/2)=sqrt((1-√2/2))/2) =sqrt((2-√2)/4) =sqrt(2-√2)/2 .. tan 67.5=tan 135/2=sin 135/(1+cos 135) =(√2/2)/1+(-√2/2) =√2/2)/1-(√2/2)) =√2/(2-√2) Note: ( + answers selected for sin & cos because 67.5º is in quadrant I where sin & cos are positive) http://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.444897.html

asnaseer · Answer

@Lulu212 now use the fact that:$$\tan(\theta)=-\tan(180-\theta)$$to see what you get for $\tan(135)$

anonymous · Answer

@asnaseer  he asks for the tangant half angle formula???

asnaseer · Answer

I'm getting there @Yahoo! - be patient. :)

anonymous · Answer

OK!..

asnaseer · Answer

@Lulu212 can you answer my question above ^^^ ?

anonymous · Answer

180 - theta = 135  

find theta?

asnaseer · Answer

not quiet:$$\tan(135)=-\tan(180-135)=-\tan(45)=?$$@Lulu212 do you know what the $\tan(45)$ is equal to?

asnaseer · Answer

@Lulu212 I can only help you here if you respond to my questions.