Question

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Calculate cos 60° in terms of other trignometric ratios.

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Answer 1

Solution :-

Let ABC be an equilateral triangle whose each side is 2a By Geometry each angle of Triangle is 60° Let AD is perpendicular to BC From Geometry ,

AD bisects Triangle BAC also bisects side BC

So, angle CAD = angle BAD = 30° and CD = BD =a

In a right angle triangle ADC ,

AD² + DC² = AC²

AD² +(a)² = (2a)²

AD² +a² = 4a²

AD² = 4a² - a²

AD² = 3a²

AD = √3a

From Right angle Triangle ADC

We know that ,

cosA = adjacent side toA / hypotenuse

Here the adjacent side is 'a'

Hypotenuse is 2a

So, cos60° = adjacent side/ hypotenuse

cos60° = a/2a

cos60° = 1/2

___________________

Know more :-

Trignometric Identities :-

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

csc²θ - cot²θ = 1

Trigonmetric relations:-

sinθ = 1/cscθ

cosθ = 1 /secθ

tanθ = 1/cotθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

Trigonmetric ratios:-

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

cotθ = adj/opp

cscθ = hyp/opp

secθ = hyp/adj