Carilah nilai keenam perbandingan trigonometri untuk sudut lancip jika berlaku cot 2/3 ?
Matematika
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Pertanyaan
Carilah nilai keenam perbandingan trigonometri untuk sudut lancip jika berlaku cot 2/3 ?
2 Jawaban
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1. Jawaban LOVEJOY
cot x = 2/3
sin x = 3/√13
cos x = 2/√13
tan x = 3/2
csc x = √13/3
sec x = √13/2 -
2. Jawaban whongaliem
cot x = 2/3
a) cot² x + 1 = cosec² x
(2/3)² + 1 = cosec² x
4/9 + 1 = cosec² x
13/9 = cosec² x
cosec x = √(13/9)
cosec x = (1/3)√13
b) cosec x = 1/sin x
(√13) /3 = 1/sin x
sin x = 3/√13
sin x = (3/13)√13
c) sin² x + cos² x = 1
{(3/13)√13)² + cos² x = 1
9/13 + cos² x = 1
cos² x = 1 - 9/13
cos² x = 4/13
cos x = √(4/13)
cos x = (2/13)√13
d) sec x = 1/cos x
= 1/ (2/√13)
= (√13) / 2
= (1/2)√13
e) tan x . cot x = 1
tan x . 2/3 = 1
tan x = 3/2