Question

Express sin theta in terms of secant theta​

Answer 1

sin theta = root(1-sec^2theta)/sec thetha

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Answer 2

Sin theta in terms of secant theta can be expressed as

$\frac{ \sqrt{ {(sec}^{2})theta - 1}}{sec \: theta}$

Given:

We have been given an angle in terms of sine.

To Find:

we need to express the angle in terms of secant.

Solution:

To do this problem, we need to know the basic trigonometric formulas and identities.

Let us assume theta as alpha for convenience.

${sin}^{2} \alpha + { \cos }^{2} \alpha = 1$

$\sin( \alpha) = \sqrt{1 - { \cos }^{2} \alpha }$

we know that

$\cos( \alpha ) = \frac{1}{ \sec( \alpha ) }$

$\sin( \alpha ) = \sqrt{1 - \frac{1}{ { \sec }^{2} \alpha } }$

$\sin( \alpha ) = \sqrt{ \frac{ { \sec }^{2} \alpha - 1}{ { \ \sec }^{2} \alpha } }$

$\sin( \alpha ) = \frac{ \sqrt{ { \sec }^{2} \alpha - 1} }{ \sec( \alpha ) }$

Therefore, sin theta can be expressed in secant theta as $\frac{ \sqrt{ {(sec}^{2})theta - 1}}{sec \: theta}$

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