oblicz sinx i cosx jeśli tgx=12/15.... Question from @madzialena271993

madzialena271993 @madzialena271993

October 2018 2 29 Report

oblicz sinx i cosx jeśli tgx=12/15

$tgx=\frac{12}{15}\\ \frac{sinx}{cosx}=\frac{12}{15}\\ 15sinx=12cosx\\ sinx=\frac{12}{15}cosx$

$sin^2x +cos^2x =1 \\ (\frac{12}{15}cosx)^2 + cos^2x=1 \\ \frac{144}{225}cos^2x +cos^2x=1\\ \frac{369}{225}cos^2x=1 \\ cos^2x=\frac{225}{369}\\ cosx= \frac{15}{3\sqrt{41}}\ v\ cosx=\frac{15}{-3\sqrt{41}}$

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1 votes Thanks 1

poziomka777

sin²α+cos²α=1

cosα=√[1-sin²α]

tgα=sinα/cosα

sinα/cosα=12/15

15sinα=12cosα

15sinα=12√[1-sin²α] /²

225sin²α=144-144sin²α

225sin²α+144sin²α=144

369sin²α=144

sinα=√[144/369]

sinα=12/3√41=4√41/41

..................................

sinα/cosα=tgα

4√41/41/cosα=12/15

cos α=5√41/41

1 votes Thanks 2

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