Smolenskayaa
Это примеры на знание таблиц приведения тригонометрических функций. 1. а) cos(5pi/2 - a) = cos(2pi + pi/2 - a) = cos(pi/2 - a) = sin a б) sin(3pi + a) = sin(2pi + pi + a) = sin(pi + a) = -sin a в) cos(7pi/2 + a) = cos(2pi + pi + pi/2 + a) = cos(pi + pi/2 + a) = = -cos(pi/2 + a) = -(-sin a) = sin a
2. 2sin(7pi/2 - a) - 5cos(17pi - a) = 2sin(2pi+pi+pi/2+a) - 5cos(16pi+pi-a) = = 2sin(pi+pi/2+a) - 5cos(pi-a) = -2sin(pi/2+a) - 5(-cos a) = -2cos a + 5cos a = = 3cos a = 3*(-0,3) = -0,9
3.[3cos(pi/2 + a) + 2sin(pi - a)] / [2cos(pi + a) - 3sin(3pi/2 + a)] = = (-3sin a + 2sin a) / (-2cos a - 3(-cos a)) = -sin a/cos a = -tg a = -4
Answers & Comments
1. а) cos(5pi/2 - a) = cos(2pi + pi/2 - a) = cos(pi/2 - a) = sin a
б) sin(3pi + a) = sin(2pi + pi + a) = sin(pi + a) = -sin a
в) cos(7pi/2 + a) = cos(2pi + pi + pi/2 + a) = cos(pi + pi/2 + a) =
= -cos(pi/2 + a) = -(-sin a) = sin a
2. 2sin(7pi/2 - a) - 5cos(17pi - a) = 2sin(2pi+pi+pi/2+a) - 5cos(16pi+pi-a) =
= 2sin(pi+pi/2+a) - 5cos(pi-a) = -2sin(pi/2+a) - 5(-cos a) = -2cos a + 5cos a =
= 3cos a = 3*(-0,3) = -0,9
3.[3cos(pi/2 + a) + 2sin(pi - a)] / [2cos(pi + a) - 3sin(3pi/2 + a)] =
= (-3sin a + 2sin a) / (-2cos a - 3(-cos a)) = -sin a/cos a = -tg a = -4
4. (4cos 25 - 3sin 65)/sin 115 = (4cos 25 - 3sin(90-25))/sin(90+25) =
= (4cos 25 - 3cos 25)/cos 25 = cos 25/cos 25 = 1
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