Stitz-Zeager_College_Algebra_e-book

6 hooked on conics again 841 2 2 a r 1cos is a

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ometrically. 11.4 Polar Coordinates 789 y x 4 = −3 = − 4 , and since this isn’t the tangent of one the common angles, we resort to using 3 the arctangent function. Using a reference angle approach,5 we ﬁnd α = arctan 4 is the 3 reference angle for θ. Since θ lies in Quadrant II and must satisfy 0 ≤ θ < 2π , we choose θ = π − arctan 4 radians. Hence, our answer is (r, θ) = 5, π − arctan 4 ≈ (5, 2.21). To 3 3 check our answers requires a bit of tenacity since we need to simplify expressions of the form: cos π − arctan 4 and sin π − arctan 4 . These are good review exercises and are hence 3 3 4 4 left to the reader. We ﬁnd cos π − arctan 4 = − 3 and sin π − arctan 3 = 5 , so that 3 5 4 x = r cos(θ) = (5) − 3 = −3 and y = r sin(θ) = (5) 5 = 4 which conﬁrms our answer. 5 y y S θ= 3π 2 θ = π − arctan x 4 3 x R R has rectangular coordinates (0, −3) π R has polar coordinates 3, 32 S has rectangular coordinates (−3, 4) 4 S has polar coordinates 5, π − arctan 3 Now th...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online