Graphing inverse secant and listing key features

Assume some function secθ = y. Then the secant angle θ can be found out by taking the inverse on both sides. This yields us the inverse secant function sec-1y = θ. As we know that secant of a right angled triangle can be obtained by taking the ratio of hypotenuse and adjacent side, we have another variant of its inverse function which is sec-1(hypotenuse / adjacent) = θ. We will move to the graph of inverse function and list out its key features.

The graph of inverse secant is shown below. It can also be notified as arcsec which means secant of an arc taken over the circumcircle.
graph of inverse secant

The graph shown above reflects to that of secant trig ratio. The key features which best describes inverse sec function are given below.

  • The domain of inverse secant function is (-∞, +∞).

  • The range of inverse sec is in between (0, π).

  • The secant angle of right triangle can be obtained by sec-1(hypotenuse / adjacent).

  • The graph comes from -∞ to horizontal asymptote and moves towards (-1, π).

  • The sec is undefined at π/2 and hence the inverse at that point also doesn't exist.

  • arcsecθ = arccos(1/θ).

The key features listed above explains the nature of inverse sec in the best way. Now that you are familiar with the topic, lets switch to inverse trig examples for secant function.

(1) For a right triangle, length of adjacent side is 5 units while that of hypotenuse is 7 units. Find the secant angle:

Secant angle can be obtained by the inverse formula which is θ = sec-1(hyp / adj) = sec-1(7 / 5) = 44.41. Thus the secant angle of specified triangle is equal to 44.41 degrees.

The illustration given above is meant to provide adequate information on the inverse sec formula. You can solve more practice problems on the same topic and enhance your knowledge regarding the same.

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