6. True or False. sec^-1 (0.5) is undefined. Explain your answer.

Question

Mathematics

Finn King

10 March, 06:37

6. True or False. sec^-1 (0.5) is undefined. Explain your answer.

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Answers (1)

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Gage Brennan · Answer 1

True

sec^-1 (x) = cos^-1 (1/x)

Therefore, sec^-1 (1/2) = cos^-1 (2)

If you plug cos^-1 (2) into your calculator, it is undefined. (Basically, you can never take an inverse cos of anything greater than the absolute value of 1 or - 1, the cosine of any angle, whether in degrees or in radians, is basically a ratio (adjacent over hypotenuse). Since the hypotenuse of any triangle is always greater than the length of its other two sides, you will always get a number smaller than 1. (Unless you are taking the cosine of 0, 90, 180, or 270, which you will either get 1 or zero).