Question

Tolong dijawab ya, saya tidak begitu mengerti...

1.) jika sin a = p
tentukan :
a.) sin 2a
b.) cos 2a
c.) sin 4a
d.) cos 4a

Terima Kasih :)

Answer 1

Sin a = p

sin a = depan / miring

depan = p
miring = 1
samping = √1² - p²
= √1 - p²

sin2a = 2 sina cosa
= 2 (depan / miring . samping / miring)
= 2 (p . √1 - p²)
= 2p . 2√1-p²

==========

cos2a = 1 - sin²a
= 1 - (sina)(sina)
= 1 - (depan / miring)(depan / miring)
= 1 - (p)(p)
= 1 - p²

==========

sin4a = sin(2a + 2a)
= 2 sin2a cos2a
= 2 (2 sina cosa)(1 - sin²a)
= 2 (2 depan / miring * samping / miring)(1 - (depan / miring)(depan / miring))
= 2 (2 p . √1-p²)(1 - p²)
= 2(2p - 2p³ - √1-p² - p²√1-p²)
= 4p - 4p³ - 2√1-p² - p²√1-p²
= 4p - 4p³ - (2+p²√1-p²)

==========

cos4a = cos(2a + 2a)
= 1 - sin²(2a)
= 1 - 2(2sina cosa)²
= 1 - 2(4sin²a cos²a)
= 1 - 8sin²a cos²a
= 1 - 8(p² . (√1-p²)²)
= 1 - 8(p² . (1 - p²))
= 1 - 8(p² - p⁴)
= 1 - 8p² + 8p⁴