Stitz-Zeager_College_Algebra_e-book

# The tree is about 47 feet tall 7 the lights are about

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Unformatted text preview: gles. In the table below, we summarize the values which we consider essential and must be memorized. Cosine and Sine Values of Common Angles θ(degrees) θ(radians) 0◦ 0 30◦ π 6 π 4 π 3 π 2 45◦ 60◦ 90◦ cos(θ) sin(θ) 1 0 3 2 √ 2 2 1 2 1 2 √ 2 2 √ 3 2 0 1 √ Example 10.2.3. Find the cosine and sine of the following angles. 1. θ = 225◦ 2. θ = 11π 6 π 3. θ = − 54 4. θ = 7π 3 Solution. 1. We begin by plotting θ = 225◦ in standard position and ﬁnd its terminal side overshoots the negative x-axis to land in Quadrant III. Hence, we obtain θ’s reference angle α by subtracting: α = θ − 180◦ = 225◦ − 180◦ = 45◦ . Since θ is a Quadrant III angle, both cos(θ) < 0 and sin(θ) < 0. Coupling this with the Reference Angle Theorem, we obtain: cos (225◦ ) = √ √ − cos (45◦ ) = − 22 and sin (225◦ ) = − sin (45◦ ) = − 22 . 618 Foundations of Trigonometry 2. The terminal side of θ = 11π , when plotted in standard position, lies in Quadrant IV, just shy 6 of the positive x-axis. To ﬁnd θ’s reference angl...
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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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