Stitz-Zeager_College_Algebra_e-book

# 102 the unit circle cosine and sine 1022 631

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Unformatted text preview: convert 0.26 61 = 15.6 . Hence, 1◦ 111.371◦ = = = = = 111◦ + 0.371◦ 111◦ + 22.26 111◦ + 22 + 0.26 111◦ + 22 + 15.6 111◦ 22 15.6 Rounding to seconds, we obtain α ≈ 111◦ 22 16 . 10.1 Angles and their Measure 597 2. To convert β to decimal degrees, we convert 28 it all together, we have 37◦ 28 17 1◦ 60 = 7◦ 15 and 17 1◦ 3600 = 17 ◦ 3600 . Putting = 37◦ + 28 + 17 7◦ 15 134897 ◦ 3600 37.471◦ = 37◦ + = ≈ + 17 ◦ 3600 3. To sketch α, we ﬁrst note that 90◦ < α < 180◦ . If we divide this range in half, we get 90◦ < α < 135◦ , and once more, we have 90◦ < α < 112.5◦ . This gives us a pretty good estimate for α, as shown below.6 Proceeding similarly for β , we ﬁnd 0◦ < β < 90◦ , then 0◦ < β < 45◦ , 22.5◦ < β < 45◦ , and lastly, 33.75◦ < β < 45◦ . Angle α Angle β 4. To ﬁnd a supplementary angle for α, we seek an angle θ so that α + θ = 180◦ . We get θ = 180◦ − α = 180◦ − 111.371◦ = 68.629◦ . 5. To ﬁnd a complementary angle for β , we seek an angle γ so that β + γ = 90◦ . We get γ = 90...
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## This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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