If the terminal side of angle θ passes through a point on the unit circle in the first quadrant where y=2√2, what is the exact measure of θ? Give your answer in radians.
Answers
Answer:
Please double check the question
y = 2√2 is not on the unit circle
The exact measure of the angle is 45°. If the terminal side of angle θ passes through a point on the unit circle in the first quadrant where y=2√2,
How to get the angle?A Unit circle is defined as a circle having a radius of 1 unit and having its center at the origin.
We know that the terminal side passes through a point of the form (√2/2, y).
Notice that the point is on the unit circle, so its module must be equal to 1, so we can write:
[tex]1=\sqrt{(\dfrac{\sqrt{2}}{2})^2+y^2}[/tex]
[tex]1^2=\dfrac{2}{4}+y^2[/tex]
[tex]1-\dfrac{1}{2}=y^2[/tex]
[tex]Y=\dfrac{1}{\sqrt{2}}[/tex]
We know that y is positive because the point is on the first quadrant.
Now, we know that our point is:
(√2/2, 1/√2)
And we can rewrite:
√2/2 = 1/√2
So the point is:
( 1/√2, 1/√2)
Finally, remember that a point (x, y), the angle that represents it is given by:
θ = Atan(y/x).
Then in this case, we have:
θ = Atan(1/√2/1/√2) = Atan(1) = 45°
If you want to learn more about angles, you can read:
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Related Questions
Which expression is equivalent to 3.5 B +4.5+0.5 B -0.5-1.5 B?
Answers
Answer:
+4.5B+0.5B-1.5B+0.5‐0.5+0.5
[(3 x 8) + 2?] + 6 - 2 Write out the steps Jayden will have to take in the yellow box? what are the steps?
Answers
Answer:
[(3*8)+2]+6-2
PEMDAS
There are parentheses so solve what is in them
3*8=24
[24+2]
26+6-2
Do the addition
32-2
30 is your answer
30 steps
help extremely quick plsssssssssssssssssssssssssssssssssss
Select all the expressions that have a value of 180 when b = 4.
A. 87b - 179 + 957 ÷87
B. 33b/12
C. b² + 120
D. 51b - 24
E. 11b + 187 - 2,756 ÷ 13
Answers
Answer:
A and E
Step-by-step explanation:
What are equivalent ratios for 32/8
Answers
Hey there!
32/8
= 32 ÷ 8 / 8 ÷ 8
= 4 / 1
Therefore, your answer should be: 4:1 or 4/1
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
please help..........
THANKS!
Answers
1
21314 JEG B 10
3
Which is the best estimate of -14
of-14; (-20)
ם
10
-42
-28
OOOO
28
42
Answers
Step-by-step explanation:
OOOO
BYE
In a bag of 50 marbles, 15 marbles are green or red.
What percentage of marbles are green or red?
Enter the missing values in the boxes to complete the ratio table.
Part____ Whole 50
Part____ Whole 100
Answers
Answer:
28% are green or red
Step-by-step explanation:
As the average daily temperature in New York City decreases, the number of persons who are observed wearing sweaters in the workplace increases. This is an example of a __________ correlation. a. causal b. zero c. positive d. negative
Answers
When the average daily temperature in New York City decreases, the number of persons who are observed wearing sweaters in the workplace increases, this implies a negative correlation.
Negative correlation simply means the relationship between two variables where as one variable increases, the other variable will reduce.
Therefore, in a situation where the average daily temperature in New York City decreases and the number of persons who are observed wearing sweaters in the workplace increases, this illustrates a negative correlation.
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One integer is 2 less than another. The sum of their squares is 34. Find the integers.
Answers
Answer:
no se bro no se inglés así no se que bas a aaer
Step-by-step explanation:
pero puedes consultar por
The temperature of a substance in an experiment changes by −8.7°F from 10 a.m. to 1 p.m. At 5 p.m., the temperature is 33.5°F. It is 23 of what the temperature was at 1 p.m.
What was the temperature at 10 a.m. of the substance?
Enter your answer as a decimal in the box.
°F
Answers
Answer: 33.5
Step-by-step explanation:
the answer is: 58.95
i took the test
Which expression represents 81 decreased by an unknown number?
81÷a
81a
81−a
81 + a
Answers
Answer:
81 - a
Step-by-step explanation:
Decreased
means to subtract
81 –
by an unknown number
means a variable such as a or x
therefor
81 – a
а (b) Two ovens are used to bake banana cakes and chocolate cakes. Each oven will ding according to its setting time. A banana cake takes 50 minutes to bake wbile a chocolate cake takes 45 minutes to bake.
(i) If each cake is put into the ovens at the same time, what is the time taken until both ovens ding simultaneously?
(ii) When the both ovens ding, how many banana cakes and chocolate cakes are baked?
Answers
Answer:
(b)(i) LCM of 45 and 50 = 450
Hence, it take 450 minutes until both ovens ding simultaneously.
(b)(ii) 450÷50=9 banana cakes baked
450÷45=10 chocolate cakes baked.
The angle of elevation of the top of a pole as seen from a point 13 ft away from the base is double its angle of elevation as seen from a point 47 ft farther from the pole. Find the height of the pole above the level of the observer's eyes. 10) A) 34 ft B) 86 ft C) 60 ft D) 45 ft
Answers
The height of the pole above the level of the observer's eyes is 31.42 ft
Let the angle of elevation of the top of the pole from a point 47 ft away be α.
Let the angle of elevation of the top of the pole from the point 13 ft away be β.
Since the angle of elevation of a point 13 feet away is twice that from 47 ft away, we have that β = 2α.
If the height of the pole above the level of the observer's eye is h, we have that
tanβ = tan2α = h/13 and tanα = h/47
From trigonometric identities tan2α = 2tanα/(1 - tan²α)
Substituting the values of the variables into the equation, we have
tan2α = 2tanα/(1 - tan²α)
h/13 = 2h/47 ÷ [1 - (h/47)²]
Dividing through by h, we have
1/13 = 2/47 ÷ [1 - (h/47)²]
Cross-multiplying, we have
1/13 = 2/47 ÷ [1 - (h/47)²]
1 - (h/47)² = 2/47 × 13
1 - (h/47)² = 26/47
(h/47)² = 1 - 26/47
(h/47)² = (47 - 26)/47
(h/47)² = 21/47
Taking square-root of both sides, we have
h/47 = √(21/47)
Cross-multiplyng, we have
h = √(21/47) × 47
h = √(21 × 47)
h = √987
h = 31.42 ft
The height of the pole above the level of the observer's eyes is 31.42 ft
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A roller coaster can take 209 passengers around the track in 11 minutes. How many passengers can the roller coaster take around the track per minute?
Answers
10. Is it possible for a regular polygon to have 240° as the measure of each of its interior
angles?
Answers
Step-by-step explanation:
No, it is not possible for a regular polygon to have 240° as the measure of each of
its interior angles.
according to the formula:
A = 180 - (360 /n)
where A is the interior angle
therefore, the A could be less than 180°
which graph be represents the soulution set of y[tex]\leq[/tex]3/4x-4?
Answers
How many eggs are 5dozens
Answers
Answer:
60
Step-by-step explanation:
1 dozen=12 eggs. 12 ×5=60
Answer:
60
Step-by-step explanation:
dozen=12
5x12=60
Glen invited 25 people to his birthday party.
20 people attended the party and 5 people did not attend.
What percent of the people whom Glen invited did not attend the party?
Answers
Answer:
20% of the invited people did not attend
Step-by-step explanation:
5 out of 25 people invited didn't attend Glen's party. That means the following:
[tex]\frac{5}{25}[/tex] people didn't come which simplifies to [tex]\frac{1}{5}[/tex]
Multiply [tex]\frac{1}{5}[/tex] by the giant one [tex]\frac{20}{20}[/tex] so the denominator is 100 which is the denominator used to find percentages.
You end up with [tex]\frac{20}{100}[/tex]
[tex]\frac{20}{100}[/tex] = 20%
20% is the percentage of the people whom Glen invited did not attend the party.
To find the percentage of people who did not attend the party, we will divide the number of people who did not attend (5) by the total number of people invited (25), and then multiply by 100.
Percentage = (Number of people not attended / Total number of people invited) × 100
Percentage = (5 / 25) × 100
Percentage = 20%
So, 20% of the people whom Glen invited did not attend the party.
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PLS HELP GRADIENT FIRST TO ANSWER GETS BRAINLIEST
Answers
Answer:
Step-by-step explanation:
Answer:
For a;
The answer will be 3
For b;
The answer will be -4
Step-by-step explanation:
To find the gradient of the lines, you must pick 2 points on the line and then find [tex]dy/dx[/tex]
I hope this helped!
Can I have brainliest?
Have a great day/night/afternoon!
- ❤ 7272033Alt ❤
Find the equation of this line.
Answers
y=3/4x+1/4
I hope this helped :)
Answer:
Step-by-step explanation:
two points on the line are (-3,-2) and (5,4)
slope=(4-(-2))/(5-(-3)=(4+2)/(5+3)=6/8=3/4
eq. of line is
y+2=3/4(x+3)
4y+8=3x+9
4y=3x+9-8
4y=3x+1
y=3/4 x+1/4
8488.75 times 24.50 plz quick
Answers
Answer:
207,974.375
I'm not sure if you need an explanation, and I myself, am not sure I can explain it to you, so I'll just give the answer to you.
Hope this helps!
Tamara bought a $22 mailbox using a 10% off coupon David bought an identical mailbox for $19.95 at a different store
Which statement is true?
Thank you
Answers
Answer:
I don't see any statements, but Tamara paid less. She paid 19.8 after the discount. David spent a little more at 19.95
In the coordinate plane, the points A(-8, -6), B(-9, 11), and C(3. - 7) are reflected over the y-axis to the points A, B, and C', respectively. What are the coordinates of A' B', and C'?
Answers
Answer:
A' = (8,-6)
B' = (9,11)
C' = (-3,-7)
Step-by-step explanation:
When reflecting a point over the y axis, multiply the point's x coordinate by -1. Do this for each point and you have your answer.
Someone please help...I hate IXL smh
Answers
Answer:
The slope is 10.
Step-by-step explanation:
It starts at 30, then 40, then 50 and so on so forth.
That being said the answer is 10.
Also, I hate IXL as well, but, I hope I helped.
Let me know if I got it correct.
- Abigail (:
y=x+30 is the equation of the line in slope intercept form.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The points through which the line passes is (0,30) and (20,50).
Slope = 50-30/20-0
=20/20
=1
Now let us find the y intercept.
Let us consider any point (0, 30).
30=1(0)+b
b=30
Hence, y=x+30 is the equation of the line in slope intercept form.
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PLEASE HELP BRAINLIEST TO THE RIGHT ANSWER!!!!!
A 7.8 kg object is suspended by a string from the ceiling of an elevator. The acceleration of gravity is 9.8 m/s^2.
A. Determine the tension in the string if it is accelerating upward at a rate of 1.5 m/s^2. Answer in units of N.
B. Determine the tension in the string if it is accelerating downward at a rate of
1.5 m/s^2
Answers
Answer:
88.14 N
64.74 N
Step-by-step explanation:
Find the mid point or these coordinates
(-2,-7) and (6,9)
select the correct response
(4,2)
(1,2)
(2,1)
(2,4)
Answers
Answer: (2,1)
Step-by-step explanation:
Which line has a constant of proportionality between y and x of 4/3
Answers
Answer:
Line A: constant of proportionality is 4/3
Step-by-step explanation:
The equation in question is y = (4/3)x, where (4/3) is the constant of proportionality as well s the slope of the line. The only line here that has a slope greater than 1 is the blue line (A).
Phil uses the model below to help him with multiple decimals. write a multiplication equation to represent the decimal model.
Answers
Multiplication equations can be modeled using decimal models.
The multiplication equation is: [tex]\mathbf{0.50 \times 0.90 = 0.45}[/tex]
From Phil model, we have the following highlights
50 boxes are shaded vertically90 boxes are shaded horizontallySo, the multiplication expression is:
[tex]\mathbf{\frac{50}{100} \times \frac{90}{100}}[/tex]
Express as decimals
[tex]\mathbf{0.50 \times 0.90}[/tex]
Multiply
[tex]\mathbf{0.50 \times 0.90 = 0.45}[/tex]
Hence, the multiplication equation is: [tex]\mathbf{0.50 \times 0.90 = 0.45}[/tex]
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what does (-x)+(-x)+(-x)=
Answers
Answer: -3x
Step-by-step explanation:
(-x)+(-x)=-2x
-2x+(-x)=-3x
what's the lcm of 24 and 30
Answers
Answer:
120
Step-by-step explanation:
The LCM of 24 and 30 is 120. To find the least common multiple (LCM) of 24 and 30, we need to find the multiples of 24 and 30 (multiples of 24 = 24, 48, 72, 96 . . . 120; multiples of 30 = 30, 60, 90, 120) and choose the smallest multiple that is exactly divisible by 24 and 30, i.e., 120.