Avoiding Ambiguities When choosing the right triangle in
Chapter 4, Problem 4.1.1.631(choose chapter or problem)
Avoiding Ambiguities When choosing the right triangle in Example 5, we used a hypotenuse of 1. It is sometimes necessary to use a variable quantity for the hypotenuse, in which case it is a good idea to use \(x^{2}\) rather than x, just in case x is negative. (All of our definitions of the trig functions have involved triangles in which the hypotenuse is assumed to be positive.)
(a) If we use the triangle below to represent \(\theta=\sin ^{-1}(1 / x)\), explain why side s must be positive regardless of the sign of x.
(b) Use the triangle in part (a) to find \(\tan \left(\sin ^{-1}(1 / x)\right)\).
(c) Using an appropriate triangle, find \(\sin \left(\cos ^{-1}(1 / x)\right)\).
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer