Stitz-Zeager_College_Algebra_e-book

From section 114 we know w3 8 and 3 02k for integers

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Unformatted text preview: of r = 5 sin(2θ) in the θr-plane, which in this case, occurs as θ ranges from 0 to π . We partition our interval into subintervals to help π π us with the graphing, namely 0, π , π , π , π , 34 and 34 , π . As θ ranges from 0 to π , r 4 42 2 4 increases from 0 to 5. This means that the graph of r = 5 sin(2θ) in the xy -plane starts at the origin and gradually sweeps out so it is 5 units away from the origin on the line θ = π . 4 r y 5 π 4 π 2 3π 4 π x θ −5 Next, we see that r decreases from 5 to 0 as θ runs through π , π , and furthermore, r is 42 heading negative as θ crosses π . Hence, we draw the curve hugging the line θ = π (the y -axis) 2 2 as the curve heads to the origin. 806 Applications of Trigonometry r y 5 π 4 π 2 3π 4 π x θ −5 π As θ runs from π to 34 , r becomes negative and ranges from 0 to −5. Since r ≤ 0, the curve 2 pulls away from the negative y -axis into Quadrant IV. r y 5 π 4 π 2 3π 4 π x θ −5 For 3π 4 ≤ θ ≤ π , r increases from −5 to 0, so...
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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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