Question

If 5sin theta =3,then find cosec theta​

Answer 1

Answer:

Step-by-step explanation:

Given,

$5sin\theta = 3$

To Find :-

$cosec\theta =?$

Solution :-

$5sin\theta = 3$

$5\times sin\theta = 3$

Transposing 5 to R.H.S :-

$sin\theta = \dfrac{3}{5}$

We know that :-

$sin\theta = \dfrac{1}{cosec\theta}$

$\implies \dfrac{1}{cosec\theta} = \dfrac{3}{5}$

Taking Reciprocal on both sides :-

$\dfrac{1}{\dfrac{1}{cosec\theta}} = \dfrac{1}{\dfrac{3}{5}}$

$\dfrac{cosec\theta}{1} = \dfrac{5}{3}$

$cosec\theta = \dfrac{5}{3}$

Know More :-

Trigonometric Relations :-

$1) sin\theta = \dfrac{1}{cosec\theta}$

$2) cos\theta = \dfrac{1}{sec\theta}$

$3) tan\theta = \dfrac{1}{cos\theta}$

Answer 2

Question:

$5 \sin( \alpha ) = 3 \: then \: find \: \csc( \alpha )$

To Find:

$\csc( \alpha )$

Answer:

$5 \sin( \alpha ) = 3 \\ \sin( \alpha ) = \frac{3}{5 } \\ we \: know \: tha t \: \sin( \alpha ) = \frac{1}{ \csc( \alpha ) }$

$here \: we \: have \: to \: find \: the \: value \: of \: \csc( \alpha )$

$\csc( \alpha ) = \frac{5}{3}$

Answer:

$\csc( \alpha ) = \frac{5}{3}$

More Information:

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