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
Studentka2010 [4]
2 years ago
12

What coordinates on the unit circle are associated with the angle measure?

Mathematics
1 answer:
Varvara68 [4.7K]2 years ago
6 0

The tangent of the given angles are the ratios <em>y</em> to the <em>x</em> coordinate of

the point of the terminal side on the unit circle.

The correct options are;

  • \dfrac{34 \cdot \pi}{3} \Longleftrightarrow \underline{ \left(-\dfrac{1}{2}, \ -\dfrac{\sqrt{3} }{2} \right)}

  • -\dfrac{7 \cdot \pi}{4} \Longleftrightarrow \underline{ \left(\dfrac{\sqrt{2} }{2}, \ \dfrac{\sqrt{2} }{2} \right)}

  • 210^{\circ} \Longleftrightarrow \underline{ \left(-\dfrac{\sqrt{3} }{2}, \ -\dfrac{1}{2} \right)}

<h3>How to find the points on the unit circle</h3>

The tangent of an angle is given as follows;

tan (\theta) = \mathbf{ \dfrac{Opposite}{Adjacent}} = \dfrac{\Delta y}{\Delta x}

First angle

An angle given is; \mathbf{\dfrac{34 \cdot \pi}{3}}

Therefore;

tan \left(\dfrac{34 \cdot \pi }{3} \right) = \mathbf{ \sqrt{3}}

The above result can be obtained as follows;

\sqrt{3}  = \mathbf{ \dfrac{-\dfrac{\sqrt{3} }{2} }{-\dfrac{1}{2} }}

Which is obtained when we have;

\left( \Delta x, \, \Delta y\right) = \mathbf{\left(-\dfrac{1}{2}, \, -\dfrac{\sqrt{3} }{2} \right)}

Therefore

The required coordinates is therefore;

  • \dfrac{34 \cdot \pi}{3} \Longleftrightarrow \left(-\dfrac{1}{2} , \ -\dfrac{\sqrt{3} }{2} \right)

Second angle

The angle, \mathbf{-\dfrac{7 \cdot  \pi}{4}}, gives; tan \left(-\dfrac{7 \cdot \pi}{4} \right) = 1

The above value can be obtained as follows;

\mathbf{\dfrac{\dfrac{\sqrt{2} }{2} }{\dfrac{\sqrt{2} }{2} }}  = 1

Which gives;

  • -\dfrac{7 \cdot \pi}{4}  \Longleftrightarrow \left(\dfrac{\sqrt{2} }{2}, \, \dfrac{\sqrt{2} }{2} \right)

Third angle

The angle 210° gives; tan(210°) = \mathbf{\frac{1}{\sqrt{3} }}, which can be obtained as follows;

\sqrt{ \dfrac{1}{3} } = \mathbf{\dfrac{-\dfrac{1}{2} }{-\dfrac{\sqrt{3} }{2} }}

Therefore;

  • 210^{\circ} \Longleftrightarrow \left(-\dfrac{\sqrt{3} }{2}, \ -\dfrac{1}{2} \right)

Learn more about the unit circle here:

brainly.com/question/1673530

You might be interested in
What is the slope of the line that passes through (-2,5) and (1,4)?<br> -3<br> -2<br> -1/3<br> 1/3
SIZIF [17.4K]

slope = m=(y2-y1)/(x2-x1)

m= (4-5)/(1-(-2))

m= -1/(1+2)

m=-1/3

Choice C

 

7 0
3 years ago
Tile costs $28 per square meter. how much will it cost to cover the counter top with new tile?( 4.36 square meters)
marta [7]
Tile costs $28 per square meter. how much will it cost to cover the counter top with new tile?( 4.36 square meters)

28 x 4.36 = $122.08
5 0
3 years ago
The distance between -18 and 15 is equal to ______.
Lina20 [59]

Answer:

It would be equal to 15 - (18)

6 0
2 years ago
Read 2 more answers
What is the mean of the numbers 6 4 9 6 7 10 7​
Paha777 [63]

Step-by-step explanation:

Mean =sum of values /number of values

total sum ↪️ 6+4+9+6+7+10+7

number of values is 7

= 49/7

<h2> = 7 is themean</h2>
6 0
2 years ago
Plz solve . 3+ x &gt; -9
STALIN [3.7K]

Answer:

12

Step-by-step explanation:

3 + x>-9 x=12 15>-9

5 0
2 years ago
Other questions:
  • Determine the length of side C &amp;&amp; B In each of the triangles below
    10·1 answer
  • Need to answer quick
    9·1 answer
  • Hey there!<br><br> Can I get some help please ? Thanks!
    6·1 answer
  • (5 x 10-3) + (6 x 10-3)<br> 2.2 X 104
    8·1 answer
  • The figure is transformed as shown in the diagram. Describe the transformation.
    11·2 answers
  • Solve.<br> 12/n - 1 = 10/n + 3<br><br> A. n = -18<br> B. n = -23<br> C. n = -30<br> D. n = -46
    14·1 answer
  • Please help me thank you
    9·1 answer
  • In the equation 5(x2 + 6x) + 3 (y2 - 2y) = 77, complete the square on x by adding within the first parentheses. Complete the squ
    6·2 answers
  • A line has a slope of zero. Which of the following points could this line pass through?
    13·2 answers
  • Help me, please??????
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!