Kenapa 2 pangkat 0 sama dengan 1

Kenapa 2⁰ = 1 ?

2⁰ = 2^1-1
     = 2¹ x 2^-1
     = 2¹ : 2¹
     = 2 : 2
     = 1

2⁰ = 1

Logaritma

^alog b = p       artinya        a^p = b

dengan   0 < a < 1   atau   a > 1

untuk   a = 10,  a tidak ditulis, jadi log b maksudnya ¹⁰log b

untuk a = e (e = 2,7128....), ^elog a ditulis ln a (logaritma natural dari a)

 

 Sifat - sifat Logaritma

1. ^alog b + ^alog c = ^alog b c


2. ^alog b - ^alog c = ^alog $\frac{b}{c}$


3. ^alog bⁿ = n . ^alog b


4. ^alog b . ^blog c = ^alog c


5. ^alog b = $\frac{{}^{d}log\; b}{{}^{d}log\; a}$


6. ^alog b = ^anlog bⁿ


7. ^alog b = $\frac{1}{{}^{b}log\; a}$


8. ^amlog bⁿ = $\frac{m}{n}$ x ^alog b


9. a^{alog b} = b

 

Tambahan

1. log² a = log a x log a


2. log^-1 a = $\frac{1}{log\; a}$

Identitas Trigonometri

tan a = $\frac{sin\; a}{cos\; a}$

ctg a = $\frac{cos\; a}{sin\; a}$

sec a = $\frac{1}{cos\; a}$

cosec a = $\frac{1}{sin\; a}$

sin² a + cos² a = 1

1 + tan² a = sec² a

1 + ctg² a = cosec² a

Rumus Trigonometri Sudut Berelasi

Kuadran I

sin (90 - a) = cos a

cos (90 - a) = sin a

tan (90 - a) = ctg a

ctg (90 - a) = tan a 

Kuadran II

sin (180 - a) = sin a

cos (180 - a) = - cos a

tan (180 - a) = - tan a

ctg (180 - a) = - ctg a

sin (90 + a) = cos a

cos (90 + a) = - sin a

tan (90 + a) = - ctg a

ctg (90 + a) = - tan a

Kuadran III

sin (180 + a) = - sin a

cos (180 + a) = - cos a

tan (180 + a) = tan a

ctg (180 + a) = ctg a

sin (270 - a) = - cos a

cos (270 - a) = -sin a

tan (270 - a) = ctg a

ctg (270 - a) = tan a

Kuadran IV

sin (360 - a) = - sin a

cos (360 - a) = cos a

tan (360 - a) = - tan a

ctg (360 - a) = - ctg a

sin (270 + a) = cos a

cos (270 + a) = - sin a

tan (270 + a) = - ctg a

ctg (270 + a) = - tan a

Sudut Negatif 

sin (- a) = - sin a

cos (- a) = cos a

tan (- a) = - tan a

ctg (- a) = - ctg a

Pengulangan Sudut

sin (k . 360 + a) = sin a

cos (k . 360 + a) = cos a

tan (k . 360 + a) = tan a

ctg (k . 360 + a) = ctg a