Найдите значение других трех основных тригонометрических функций , если : 1) [tex]cos\alpha = - \frac{\sqrt6}{4} , \frac{\pi}{2} < \alpha < \pi [/tex]
2) [tex]sin\alpha =\frac{\sqrt2}{3} , 0 < \alpha < \frac{\pi}{2}[/tex]
3) [tex]cos\alpha=\frac{15}{17} , \frac{3\pi}{2} < \alpha < 2\pi[/tex]
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Verified answer
1) pi/2 < a < pi, поэтому sin a > 0, cos a < 0cos a = -√6/4; cos^2 a = 6/16
sin^2 a = 1 - cos^2 a = 1 - 6/16 = 10/16; sin a = √10/4
tg a = sin a / cos a = (√10/4) : (-√6/4) = -√10/√6 = -√5/√3 = -√15/3
2) 0 < a < pi/2, поэтому sin a > 0, cos a > 0
sin a = √2/3; sin^2 a = 2/9
cos^2 a = 1 - sin^2 a = 1 - 2/9 = 7/9; cos a = √7/3
tg a = sin a / cos a = (√2/3) : (√7/3) = √2/√7 = √14/7
3) 3pi/2 < a < 2pi, поэтому sin a < 0, cos a > 0
cos a = 15/17; cos^2 a = 225/289
sin^2 a = 1 - cos^2 a = 1 - 225/289 = 64/289; sin a = -8/17
tg a = sin a / cos a = (-8/17) : (15/17) = -8/15