1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lera25 [3.4K]
3 years ago
13

Plot the point whose polar coordinates are given. Then find the Cartesian coordinates of the point. (a) (5, 3π/2) (x, y) = (b) (

3 2 , π/4) (x, y) = (c) (−1, −π/6) (x, y)

Mathematics
1 answer:
Vlad1618 [11]3 years ago
6 0

Answer:

A)(5,\frac{3\pi}{2})=(0,-5)\:B)(\frac{3}{2} , \frac{\pi}{4} ) \Rightarrow (\frac{3\sqrt{2}}{4} ,\frac{3\sqrt{2}}{4} )\:C)(-1,\frac{\pi}{6})= (\frac{\sqrt{3}}{2},\frac{1}{2})

Step-by-step explanation:

1) Check the Polar Coordinates on the graph.

2) A polar coordinate is given in (r,\theta) Let's transform each polar coordinate into Cartesian one. Considering:

A)

x=rcos\theta\\y=rsin\theta\\

A) (5,\frac{3\pi}{2})\\cos(\theta)=\frac{x}{5}\\cos(\frac{3\pi}{2})=\frac{x}{5}\:Cross\: Multiplying\\x=5 cos(\frac{3\pi}{2})\\x =5 cos(0)\:x=0\\sin(\frac{3\pi}{2})=\frac{y}{5}\\y=5sin(-1)\\y=-5\\(0,-5)

B) (b) (3/2 , π/4)

B) (\frac{3}{2},\frac{\pi}{4})\\cos(\theta)=\frac{x}{\frac{3}{2}}\\\frac{3}{2}cos(\frac{\pi}{4})=x\:Cross\: Multiplying\\x=\frac{3}{2}*\frac{\sqrt{2}}{2}\\x =\frac{3\sqrt{2}}{4} \approx 1.06

y=\frac{3}{2}sin(\frac{\pi}{4})\Rightarrow y =\frac{3\sqrt{2}}{4}

B)(\frac{3}{2} , \frac{\pi}{4} ) \Rightarrow (\frac{3\sqrt{2}}{4} ,\frac{3\sqrt{2}}{4} )

C) (c) (−1, −π/6)

C) (-1,-\frac{\pi}{6})\\cos(\theta)=\frac{x}{-1}\\-cos(\frac{-\pi}{6})=x\:Cross\: Multiplying\\x=\frac{\sqrt{3}}{2}

(-1,-\frac{\pi}{6})\\sin(\theta)=\frac{x}{-1}\\-sin(\frac{-\pi}{6})=x\:Cross\: Multiplying\\x=\frac{1}{2}

C)(-1,\frac{\pi}{6})= (\frac{\sqrt{3}}{2},\frac{1}{2})

You might be interested in
I need help again lol
olya-2409 [2.1K]

Answer:

i think i answered this already

Step-by-step explanation:

lol

3 0
3 years ago
May I have help to figure out how to do this? It is confusing! :(
RSB [31]

Answer:

it should be 80%

Step-by-step explanation:

I hope this helps

3 0
3 years ago
Nadia bought 4.3 pounds of ham on Tuesday and 1.7 pounds of ham on Wednesday. She spent a total of $41.94. What was the price of
zhuklara [117]

Answer:

Step-by-step explanation:

41.94/6=6.99

6 0
3 years ago
Read 2 more answers
Find the length of MT
Mnenie [13.5K]

Answer:

Solution,

x+12+8x-2=180° (Linear pair)

or, 9x+10=180°

or, x+10=180/9

or, x=20-10

x=10

The length of MT

=8x-2

=8×10-2

=80-2

=78

hope it helps you

7 0
3 years ago
Read 2 more answers
What is the answer to this question ? Please answer !!
mylen [45]

\text{Let}\ k:y=m_1x+b_1\ \text{and}\ k:y=m_2x+b_2,\ \text{then}\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\-------------------------\\\text{We have}\ 5x-y=-4.\ \text{Convert it to the slope-intercept form:}\\\\5x-y=-4\qquad\text{subtract 5x from both sides}\\\\-y=-5x-4\qquad\text{change the signs}\\\\y=5x+4\to m_1=5\to m_2=-\dfrac{1}{5}\\\\\text{Therefore we have}\ y=-\dfrac{1}{5}x+b.\\\\\text{The line passing through the point (-2, 2).}\\\text{Put the coordinates of the point to the equation:}

2=-\dfrac{1}{5}(-2)+b\\\\2=\dfrac{2}{5}+b\qquad\text{subtract}\ \dfrac{2}{5}\ \text{from both sides}\\\\1\dfrac{3}{5}=b\to b=\dfrac{8}{5}\\\\\text{Therefore we have the equation of a line in slope-intercept form:}\\\\y=-\dfrac{1}{5}x+\dfrac{8}{5}\\\\\text{Convert it to the standard form}\ Ax+By=C:\\\\y=-\dfrac{1}{5}x+\dfrac{8}{5}\qquad\text{multiply both sides by 5}\\\\5y=-x+8\qquad\text{add x to both sides}\\\\\boxed{x+5y=8}\to\boxed{[B]}

8 0
3 years ago
Other questions:
  • Ellen makes and sells bookmarks. She graphs the number of bookmarks sold compared to the total money earned. What is the rate of
    10·2 answers
  • It is in the attachment.
    15·1 answer
  • How do you say (98-78)×11
    15·2 answers
  • Whats the greatest common factor of 20 and 40
    7·2 answers
  • Use the distributive property to write an expression equivalent to 5✖️(3+4)
    10·2 answers
  • Which is a true statement?
    15·2 answers
  • Name an inscribed angle that intercepts arc AB.
    15·1 answer
  • Write an expression that is equivalent to 9.7 – 3.2 
    12·1 answer
  • How can u find the radius wit the height nd volume
    5·1 answer
  • Pahelp Po pls.. hina ko kase sa math hihi:,-):-)​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!