Question

)If sin θ =1/√2 then find cos θ​

Answer 1

Given :-

$\sf{ \sin \theta} =\dfrac{1}{\sqrt2}$

To find :-

$\sf{ \cos\theta}$

Solution:-

Method :- 1

We know the identity

sin²A + cos² A = 1

cos²A = 1- sin²A

$\sf{ \sin\theta} =\dfrac{1}{\sqrt2}$

$\sf \sin^2 \theta = \dfrac{1}{ \sqrt{(2)}^{2}}$

$\sf{\sin^2\theta} = \dfrac{1}{2}$

So,

cos²A = 1- sin²A

$\sf{\cos^2\theta} = 1 - \dfrac{1}{2}$

$\sf{\cos^2\theta} = \dfrac{1}{2}$

$\sf{\cos\theta}$ = $\sqrt{ \dfrac{1}{2} } = \dfrac{1}{ \sqrt{2} }$

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Method - 2 :-

Observe the attachment

sinA = opp/ hyp

cosA = adj/hyp

So,

We can find adjacent side by pythagoras theoram

AB² + BC² = AC²

(1)² + BC² = $( \sqrt{2} )^{2}$

1 + BC² = 2

BC² = 2-1

BC² = 1

BC = 1

Now , cos A = adj/hyp

cos A = BC/ AC

$\sf{\cos\theta}$ = 1/$\sf\sqrt{2}$

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Know more :-

Trigon metric Identities

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

csc²θ - cot²θ = 1

Trigometric 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