Trigonometri (1)

1. perkalian trigonometri

1.1. Sin A cos B = 1/2 [sin (A+B) + sin(A+B) ]

1.2. Cos A sin B = 1/2 [sin (A+B) - sin (A-B)]

1.3. Cos A cos B = 1/2 [cos (A+B)+cos (A-B)]

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2. Turunan trigonometri

2.1. y=sin x | y'=cos x

2.2. y=cos x | y'= -sin x

2.3. y=tan x | y'= sec2x

2.4. y=cot x | y'= -csc2x

2.5. y=sec x | y'= sec x tan x

2.6. y=csc x | y'= - csc x cot x

3. persamaan trigonometri

3.1. sin x = sin a ~ x = a + k. 360 x =(180 - a) + k . 360

3.2. cos x = cos a ~ x = a + k . 360 x = -a + k . 360

3.3. tan x = tan a ~ x = a + k . 180

4. penjumlahan trigonometri

4.1. sin A + sin B = 2 sin (A+B/2) cos ( A-B/2)

4.2. sin A - sin B = 2 cos (A+B/2) sin (A-B/2)

4.3. 2 sin A cos B =sin( a+b)+sin(a-b)

4.4. -2sin A sin B= cos (a+b)-cos (a-b)

4.5. 2 cos A sin B= sin(a+b)- sin (a-b)

4.6. 2 cos A cos B= cos (a+b)+cos (a-b)

5. Aplikasi turunan trigonometri

5.1. fungsi naik dan fungsi turun

5.1.1. fungsi naik pada saat f'(x) > 0

5.1.2. fungsi turun pada saat f'(x) < 0

5.2. garis singgung

5.2.1. y-y1 = m (x-x1)