Write down the next term in this sequence -1 2 7 14 23
1 answer:
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For two ratios to form a proportion they have to be equal.
To see if two ratios are equal we express them in their simplest form.
In this case we notice that in the first ratio both numbers are multiples of five, then:
In the second case we notice that both numbers are multiples of 2, then:
Since both ratios can be simplified to the same final ratio, they form a proportion.
X = 18°
cos 54° = sin 36°
cos 3 x = sin 2 x
cos ( 2 x + x ) = sin 2 x
cos 2 x cos x - sin 2 x sin x = 2 sin x cos x
( cos² x - sin² x ) cos x - 2 sin² x cos x = 2 sin x cos x / : cos x
( divide both sides by cos x )
cos² x - sin² x - 2 sin² x = 2 sin x
1 - sin² x - 3 sin² x - 2 sin x = 0
- 4 sin² x - 2 sin x + 1 = 0 substitution: u = sin x
- 4 u² - 2 u + 1 = 0
u = 2 -√20 / - 4 sin 18° = (√ 5 - 1 )/4
cos 18° = √( 1² - ((√5 - 1)/4)²
cos 18° = (10+2√5)^(1/2) / 4
cos 54° = sin 36°
cos 3 x = sin 2 x
cos ( 2 x + x ) = sin 2 x
cos 2 x cos x - sin 2 x sin x = 2 sin x cos x
( cos² x - sin² x ) cos x - 2 sin² x cos x = 2 sin x cos x / : cos x
( divide both sides by cos x )
cos² x - sin² x - 2 sin² x = 2 sin x
1 - sin² x - 3 sin² x - 2 sin x = 0
- 4 sin² x - 2 sin x + 1 = 0 substitution: u = sin x
- 4 u² - 2 u + 1 = 0
u = 2 -√20 / - 4 sin 18° = (√ 5 - 1 )/4
cos 18° = √( 1² - ((√5 - 1)/4)²
cos 18° = (10+2√5)^(1/2) / 4