Question

If cos theta=x/y, find cosec theta

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

The value of cosec θ is $\frac{y}{\sqrt{y^{2}-x^{2}}}$.

Step-by-step explanation:

In a right angled triangle the formula of cos θ and sin θ are:

$cos \theta=\frac{b}{h}\ \ \ \ \ \ \ \ \ sin\theta=\frac{p}{h}$

Here

p = perpendicular

b = base

h = hypotenuse

Given:

$cos\theta=\frac{x}{y}$

Compute the value of the perpendicular using the Pythagoras theorem as follows:

$h^{2}=p^{2}+b^{2}\\y^{2}=p^{2}+x^{2}\\p^{2}=y^{2}-x^{2}\\p=\sqrt{y^{2}-x^{2}}$

Compute the value of sin θ as follows:

$sin\theta=\frac{p}{h}=\frac{\sqrt{y^{2}-x^{2}}}{y}$

Compute the value of cosec θ as follows:

$cosec\theta=\frac{1}{sin\theta}=\frac{y}{\sqrt{y^{2}-x^{2}}}$

Thus, the value of cosec θ is $\frac{y}{\sqrt{y^{2}-x^{2}}}$.