Jawaban:

Persamaan Trigonometri

Penjelasan dengan langkah-langkah:

1. -√(3) Sin x + Cos x = √(2)

a=-3 b=1

r=√(-3)²+(1)²

=√(9)+1

=√(10)

tan p = b/a

tan p = 1/-√(3)

= -√(3)/3

= -1/3√(3)

tan -30 = -1/3√(3) => ( kuadran IV )

r Cos (x-p)=√(2)

√(10) Cos (x-(-30)=√(2)

√(10) Cos (x+30)=√(2)

Cos (x+30)=√(2)/√(10)

Cos (x+30)=√(2)x√(10)/√(10)x√(10)

Cos (x+30)=√(20)/10

Cos (x+30)=√(4x5)/20

Cos (x+30)=2√(5)/20

Cos (x+30)=√(5)/10

Cos (x+30)=1/10√(5)

Cos (x+30)=Cos 77,079⁰

(x+30)=77,079⁰

(x)=77,079⁰-30⁰

(x)=47,079⁰

atau

Cos (x+30)=Cos 282,921⁰

(x+30)=282,921

(x)=282,921-30

(x)=252,921⁰

HP=(47,079⁰ , 252,921⁰)

2. √(3) Sin x - Cos x =√(3)

a=√(3) b=-1

r=√(√(3)²+(-1)²

=√(3)+1

=√(4)

=2

tan p = b/a

= -1/√(3)

= -√(3)/3

= -1/3√(3)

tan -30 = -1/3√(3) => (kuadran IV)

r Cos (x-p)=√(3)

2 Cos (x-(-30)=√(3)

2 Cos (x+30)=√(3)

Cos (x+30)=√(3)/2

Cos (x+30)=1/2√(3)

Cos (x+30)=Cos 30

(x+30)=30

(x)=30-30

(x)=0⁰

atau

Cos (x+30)= Cos 330

(x+30)=330

(x)=330-30

(x)=300⁰

HP=(0⁰, 300⁰)

3. Cos x +√(3) Sin x = 1

a=1 b=√(3)

r=√(1)²+√(3)²

=√(1)+3

=√(4)

=2

tan p = b/a

= √(3)/1

= √(3)

tan 60 = √(3) => (kuadran I)

r Cos(x-p)=1

2 Cos(x-60)=1

Cos(x-60)=1/2

Cos(x-60)=Cos 60

(x-60)=60

(x)=60+60

(x)=120⁰

atau

Cos (x-60)=Cos 300

(x-60)=300

(x)=300+60

(x)=360⁰

HP=(120⁰, 360⁰)

Demikian

Semoga membantu dan bermanfaat!