Trig Quiz Chapter 6c

Find the rectangular coordinate of (-3, -29pi/7)

(-2.70, 1.30)

Find all polar coordinates of polar coordinate (1.5, -20 degrees) for -2pi <= x <=2pi

(1.5 , -pi/9) (-1.5, -10pi/9) (-1.5, 8pi/9) (1.5, 17pi/9)

Find all polar coordinates of polar coordinate (2, pi/6) for -2pi <= x <=2pi

1. (2, pi/6) 2. Draw a picture of scenario 1rst quadrant and postive number 3. (-2, 7pi/6) 4.(2, - 11pi/6) 5.(-2, -5pi/6)

Plotting points with given polar coordinate (-1 , 2pi/5)

1. Draw picture and convert 2pi/5 to degree 2pi/5 = 72 degrees 1rst quadrant 2. Then draw from magnitude 0 backwards -1 Dot is placed in 3rd quadrant because magnitude is negative

Plotting points with given polar coordinate (3, 4pi/3)

1. Draw picture and find 4pi/3 3rd quadrant 60 angle 2. Then go magnitude from 0 length of 3

Plotting points with given polar coordinate

1. If negative magnitude, draw backwards 2. If negative angle start from 0 going backwards

Find the rectangular coordinate of (3, 2pi/3)

1. Use formula x = r*cos(theta) and y = r*sin(theta) x = 3 * cos(2pi/3), y = 3* sin(2pi/3) x = 3 *-1/2, y = 3*sqrt(3) /2 x = -3/2, y= 3*sqrt(3) / 2

Find the rectangular coordinate of (-2, 60)

1. Use polar to rectangular formula x= r*cos(theta) y = r*sin(theta) x = -2 * cos 60 ; y = -2 * sin 60 x = -2 * 1/2 ; y = -2 * sqrt(3)/2 x = -1 ; y = -sqrt(3)

Covert polar equation to rectangular equation and identify the graph r= -3 sin(x)

1. When cos or sin is used multiply by r r *r = -3 r sin(x) r^2 = -3rsin(x) 2. r^2 turns into x^2 + y^2 and rsin(x) = y x^2 + y^2 = -3y 3. Add 3y x^2 + y^2 +3y ______ = 0 4. Complete the square x^2 + (y + 3/2)^2 = 9/4 A circle at center ( 0, -3/2) with radius of (3/2)

Covert polar equation to rectangular equation and identify the graph r cscx = 1

1. When cscx or secx is on the left then -divide by csc or sec -Multiply by r -Simplify r = 1/csc x r = sin x r^2 = rsinx x^2 + y^2 = y X^2 + Y^2 + y = 0 x^2 + (y - 1/2)^2 = 1/4

Covert polar equation to rectangular equation and identify the graph r= 3 sec(x)

1. When sec or csc are used multiply by cos or sin respectivly r * cos(x) = 3sec(x) * cos(x) x = 3 Vertical line at x = 3

Going from rectangular coordinates to polar coordinates

Given (x,y) find (r, x) r = sqrt( (x)^2 + (y)^2 ) x = tan-1 (y / x) x can be multiple things in polar coordinates, so draw a picture with the angle found. restriction -2pie < x <2pie

Convert the rectangular equation to polar form 2x - 3y = 5

If given both x and y, and not a circle then - convert x and y to r format - factor out r - divide by what is left in parentheses 2x - 3y = 5 2rcos x - 3rsin x = 5 r(2cosx - 3sinx) = 5 r = 5/(2cosx - 3sinx)

Convert the rectangular equation to polar form (x-3)^2 + (y+3)^2 = 18

If given in circular form then -Factor -Simplify and subtract constant to get right side = 0 -Combined x^2 and y^2 to make r^2 -Make other variables their respective r form -Divide by r -Get r alone (x-3)(x-3) + (y+3)(y+3) = 18 x^2 - 6x + 9 + y^2 +6y + 9 = 18 x^2 + y^2 - 6x + 6y = 0 r^2 - 6rcosx + 6rsinx = 0 r - 6cosx + 6sinx = 0 r = 6cosx - 6sinx

Convert the rectangular equation to polar form (x-3)^2 + y^2 = 9

If given in circular form then -Factor -Simplify and subtract constant to get right side = 0 -Combined x^2 and y^2 to make r^2 -Make other variables their respective r form -Divide by r -Get r alone (x-3)(x-3) + y^2 = 9 x^2 -6x + 9 + y^2 = 9 x^2 + y^2 -6x = 0 r^2 -6rcosx = 0 r - 6cosx = 0 r = 6cosx

Convert the rectangular equation to polar form x = 2

If given x or y change to its respective r format rcosx = x rsinx = y x = 2 rcosx = 2 r = 2/cosx r = 2 * 1/cosx r = 2 sec x

Find the rectangular coordinate of (1.5 , 7pi/3)

Memorized angle denoms are 6,4,3 (3/4, 3sqrt(3)/4)

When asked to match a polar equation with its graph ...

make sure you are in polar mode, and radians are set

Going from polar coordinates to rectangular coordinates...

x = r * cos(x) y = r* sin(x) 1. If an known angle measurement, use an exact value.