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Stitz-Zeager_College_Algebra_e-book

3 5 111 applications of sinusoids 755 it is possible

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Unformatted text preview: we divide the side view of the house down the middle, we ﬁnd that the roof line forms the hypotenuse of a right triangle with legs of length 6 feet and 12 feet. Using Theorem 6 10.10, we ﬁnd the angle of inclination, labeled θ below, satisﬁes tan(θ) = 12 = 1 . Since θ is an 2 1 acute angle, we can use the arctangent function and we ﬁnd θ = arctan 2 radians. Converting degrees to radians,7 we ﬁnd θ = arctan 1 2 radians 180 degrees π radians ≈ 26.56◦ . 6 feet θ 12 feet 10.6.4 Solving Equations Using the Inverse Trigonometric Functions. In Sections 10.2 and 10.3, we learned how to solve equations like sin(θ) = 1 for angles θ and 2 tan(t) = −1 for real numbers t. In each case, we ultimately appealed to the Unit Circle and relied on the fact that the answers corresponded to a set of ‘common angles’ listed on page 619. If, on the other hand, we had been asked to ﬁnd all angles with sin(θ) = 1 or solve tan(t) = −2 for 3 real numbers t, we would have been hard-pressed to do so. With the introduction of the inverse trigon...
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