Algebra/Trig Review - Pauls Online Math Notes - Lamar University

Algebra/Trig ReviewIn the case of inverse trig functions we are after a single value. We don’t want tohave to guess at which one of the infinite possible answers we want. So, to make surewe get a single value out of the inverse trig cosine function we use the followingrestrictions on inverse cosine.( x)−1θ = cos −1 ≤ x≤1 and 0 ≤θ ≤ πThe restriction on the θ guarantees that we will only get a single value angle andsince we can’t get values of x out of cosine that are larger than 1 or smaller than -1 wealso can’t plug these values into an inverse trig function.So, using these restrictions on the solution to Problem 1 we can see that the answer inthis case iscos⎛ 1 3 ⎞ − = π⎜⎝2 ⎟⎠ 62.cos⎜−⎝⎛ −1 3 ⎞2⎟⎠SolutionIn general we don’t need to actually solve an equation to determine the value of aninverse trig function. All we need to do is look at a unit circle. So in this case we’re3after an angle between 0 and π for which cosine will take on the value − . So,2check out the following unit circle© 2006 Paul Dawkins 78http://tutorial.math.lamar.edu/terms.aspx