The inverse trigonometric functions are the inverse functions of the trigonometric functions, written, like sin inverse x, cos inverse x, tan inverse x, cosec inverse x, sec inverse x, cot inverse x. y = Sin inverse x can also be read as y is the arc sin x and it means that y is the real number angle whose sine value is x. The domain of the inverse cosine function is [–1, 1] and the range is [0, π].
Example1: i ) Evaluate y = arc sin(- 1/2).
ii) Evaluate y = arc tan (- 1).
Solution: ) We first need to find those angles whose sine values is equal to – 1/2 .The answer must be in the principle range of - pi/2 less than equal to y less than equal to pi/ 2.So the answer is - pi / 6 .
ii ) We first need to find those angles whose tan values is equal to – 1 .The answer must be in the principle range of – pi /2 less than y less than pie/2 . So the answer is - pi / 4.
Example2: If the lengths of the two legs of a right triangle ABC are BC = 7 and AC = 10, find the measure of the largest acute angle.
Solution:Acute angle B is larger than angle A since the side opposite to angle B (side AC = 10) is larger than the side opposite to angle A (side BC = 7).
angle B = arc tan (10 / 7)
angle B= 55 degrees.