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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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