Trigonometry Assignment

Assignment
Trigonometry
<STUDENT NAME>
APRIL 15, 2019

Problem 1. SHOW ALL WORK. Given the polar point (4, -19π/6)
1A. Find two other polar expressions for the point, one with a negative r value, and another with a
positive r value. Use exact values.
4 ( cos ( −19 π
6 ) i +sin ( −19 π
6 ) j )
4 (− √3
2 i + 1
2 j )
¿−4 ( √3
2 i− 1
2 j )= (−4 , 11 π
6 )
4 (− √3
2 i+ 1
2 j )= (4 , 5 π
6 )
1B. Convert the polar point (4, -19π/6) into rectangular coordinates (x,y). Compute the
coordinates exactly.
Polar point is given by r (icos θ+ j sin θ)
r =4
θ= π
6
4 ( − √ 3
2 i+ 1
2 j )=−3.464 i+2 j
( x , y ) =(−3.46,2)
Problem 2. Fill in the blanks in the listed polar points (r, θ) below, to satisfy the polar function
r = 1 – 6cos(2θ). Find all of these points exactly.
 Given θ = π, find r: ( ____, π)
Sol.
Given r=1−6 cos 2 θ
r =1−6 cos−1 2 π
r =1−6
r =−5
 Given θ = π/8, find r: ( ¿¿, π/8)
Sol.
Given r=1−6 cos 2 θ

r =1−6 cos−1 2 π
8
r =1−6 cos π
4
r =1−6( 1
√ 2 )
r =1−3 √2=−3.24
 Find one specific point. Given r = 4, find θ: ( 4,____)
Sol.
Given r=1−6 cos 2 θ
4=1−6 cos 2 θ
cos 2 θ=−1
2
2 θ=cos−1 −1
2
2 θ= 2 π
3
θ= π
3
 Graph the polar function r = 1 – 6cos(2θ). Locate and label on your graph the three points
you found above in problem 2A.
Sol.