Understanding the Reciprocal Identity for Cosine (cos θ) and its Applications in Trigonometry

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The reciprocal identity for cosine (cos θ) is the ratio of the adjacent side to the hypotenuse in a right-angled triangle

The reciprocal identity for cosine (cos θ) is the ratio of the adjacent side to the hypotenuse in a right-angled triangle.

In trigonometry, cosine (cos θ) is defined as the ratio of the length of the adjacent side to the hypotenuse of a right-angled triangle. The reciprocal of cosine, denoted as 1/cos θ or sec θ, represents the ratio of the hypotenuse to the length of the adjacent side.

So, the reciprocal identity for cos θ is:

sec θ = 1 / cos θ

This identity is often used to express cos θ in terms of sec θ or vice versa. It allows us to easily switch between cosine and secant in trigonometric calculations.

For example, if we know the value of cos θ, we can find sec θ by taking the reciprocal of cos θ. Similarly, if we know the value of sec θ, we can find cos θ by taking the reciprocal of sec θ.

It’s worth noting that sec θ can also be defined as the inverse of the cosine function (arcsec θ), but the reciprocal identity specifically refers to the reciprocal ratio of the cosine function.

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