Question

Kelas 10 trigonometri

Answer 1

Nomor 1.
tan(-1200)
= -tan 1200
= -tan (1080+120)
= -tan 120
= -tan(180-60)
= -(-tan 60)
= tan 60
= √3 [B]

Nomor 2.

Maka, dengan phytagoras, didapat:


Nomor 3.


Nomor 4.
α dan β adalah sudut segitiga siku-siku.
tan α = √2 sin β
sin α/cos α = √2 sin(90-α) || Sifat segitiga siku-siku
sin α/cos α = √2 cos α
sin α = √2 cos²α
sin α = √2 - √2 sin²α
√2 sin²α + sin α - √2 = 0
2sin²α + √2 sin α - 2 = 0
(√2 sin α - 1)(√2 sin α + 2) = 0
Karena sin α = -√2 Tidak memenuhi.
Maka,
sin α = ½ √2
α = π/4
Yang mana,
sin²α = sin²(π/4) = (½√2)² = 2/4 = 1/2 [D]

Nomor 5.
Substitusikan langsung:
Tips: π = 180°
= -2 cos(2.π/3) = -2 cos 120 = -2(-1/2) = 1
= -2 cos(2.3π/4) = -2 cos 270 = -2(0) = 0
= -2 cos(2.5π/6) = -2 cos 300 = -2(1/2) = -1
Rangenya : {-1,0,1} [A]