Jawaban:

Latihan Soal

Penjelasan dengan langkah-langkah:

1. 16 8 4 1/8

a. Rasio

r = U₂/U₁

= 8/16

= 1/2

b. Banyak suku

a=16

r=1/2

Un=ar⁽ⁿ⁻¹⁾

=16.1/2⁽ⁿ⁻¹⁾

Un= 16.1/2⁽ⁿ⁻¹⁾

1/8=16.1/2ⁿ⁻¹

1/8/(16)=1/2ⁿ⁻¹

1/8x1/16=1/2ⁿ⁻¹

1/128=1/2ⁿ⁻¹

1/2⁷=1/2ⁿ⁻¹

7 = n-1

n = 7+1

n = 8

c. S₇ = a(1-rⁿ)/1-r

= 16(1-1/2⁷)/(1-1/2)

= 16(1-1/128)/(1/2)

= 16(128/128-1/128)x(2/1)

= 16(127/128)x(2)

= 32(127/128)

= 1(127/4)

= 127/4

= 31 3/4

Pembuktian

16 8 4 2 1 1/2 1/4

(16+8+4+2+1) + 1/2 + 1/4

(31)+(2/4+1/4)

(31)+(3/4)

(31 3/4)

2. Sin A = 5/13 (0⁰≤x≤90⁰)

Tan A = ...

Sin A = y/r

x,y,r

x,5,13

x=√(13²-5²)

=√(169-25)

=√(144)

= 12

Cos A = x/r

= 12/13

Tan A = Sin A/Cos A

= (5/13) / (12/13)

= (5/13)x(13/12)

= (5/12)

Tan A = y/x

= 5/12

3. BC = ...

Cos A = x/AC

Cos 30⁰ = AB/8√(3)

1/2√(3) = AB/8√(3)

AB = 1/2√(3)x8√(3)

AB = 4.3

AB = 12 cm

Sin A = y/r

Sin 30⁰ = BC/AC

1/2 = BC/8√(3)

BC = 1/2x8√(3)

BC = 4√(3) cm

4. Sin 150⁰ + Sin 120⁰

Cos 300⁰

Sin (90+60) + Sin (90+30)

Cos ( 360-60)

Cos 60 + Cos 30

Cos 60

1/2 + 1/2√(3)

1/2

1/2(1+√(3)

1/2

(1+√(3)

Demikian

Semoga membantu dan bermanfaat!