VRAE oor vraestel 2: Trig uitdrukkings

$V e r e e n v o u d i g space fraction numerator cos open parentheses 720 degree minus x close parentheses sin x plus sin x over denominator open parentheses 1 minus sin squared x close parentheses plus cos x end fraction$

(Edited by Marna Zuhlsdorff - original submission Monday, 10 February 2020, 5:05 PM)

Re: Trig

by Marna Zuhlsdorff - Friday, 21 February 2020, 1:28 AM

Hi Annette

Baie dankie vir jou vraag en bewerking. Daar is niks wat ek aan jou bewerking sou verander het nie, maar vir 'n memo vir ander mense sou ek twee goed byvoeg.

$table row cell space space space space fraction numerator cos open parentheses 720 minus x close parentheses sin x plus s i n x over denominator open parentheses 1 minus sin squared x close parentheses plus cos x end fraction end cell blank blank blank row cell equals fraction numerator c o s x. sin x plus s i n x over denominator open parentheses 1 minus sin squared x close parentheses plus cos x end fraction end cell blank blank cell asterisk times Vereenvoudig space cos open parentheses 720 minus x close parentheses end cell row cell equals fraction numerator cos x. sin x plus s i n x over denominator c o s squared x plus cos x end fraction end cell blank blank cell asterisk times asterisk times Vereenvoudig space open parentheses 1 minus sin squared x close parentheses end cell row cell equals fraction numerator sin x open parentheses cos x plus 1 close parentheses over denominator cos x open parentheses cos x plus 1 close parentheses end fraction end cell blank blank cell GGF space faktorisering end cell row cell equals fraction numerator sin x up diagonal strike open parentheses cos x plus 1 close parentheses end strike over denominator cos x up diagonal strike open parentheses cos x plus 1 close parentheses end strike end fraction end cell blank blank cell Kanselleer space uit end cell row cell equals fraction numerator sin x over denominator cos x end fraction end cell blank blank blank row cell equals tan x end cell blank blank blank end table$

$table row cell asterisk times open parentheses 720 minus x close parentheses equals cos x end cell row cell want space cos open parentheses 720 minus x close parentheses equals cos open square brackets open parentheses 720 minus x close parentheses minus 2 open parentheses 360 close parentheses close square brackets end cell row cell equals cos open square brackets 720 minus 720 minus x close square brackets end cell row cell equals cos open parentheses negative x close parentheses end cell row cell equals plus cos x end cell end table$

Jy kan altyd $360 degree$ van 'n hoek aftrek, want $360 degree$ is een omwenteling. As jy dit op 'n trig assestelsel doen, dan sal jy sien jy eindig presies op waar jy begin het, so 'niks' het regtig verander nie.

$table row cell asterisk times asterisk times 1 minus sin squared x equals cos squared x end cell row cell want space sin squared x plus cos x equals 1 end cell row cell cos squared x equals 1 minus sin squared x end cell end table$

Hier herskryf ons net die bekende graad 11 identiteit om die $1 minus sin squared x$ alleen te kry.