Question 7.5.3: Finding Inverse Function Values (Degree-Measured Angles) Fin...
Finding Inverse Function Values (Degree-Measured Angles)
Find the degree measure of θ if it exists.
(a) θ= \arctan 1 (b) θ = \sec^{-1} 2(a) Here θ must be in (-90°, 90°), but because 1 is positive, θ must be in quadrant I. The alternative statement, \tan θ = 1, leads to θ = 45°.
(b) Write the equation as \sec θ = 2. For \sec^{-1} x, θ is in quadrant I or II. Because 2 is positive, θ is in quadrant I and θ = 60°, since \sec 60° = 2. Note that 60° (the degree equivalent of \frac{π}{3} ) is in the range of the inverse secant function.
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