Complete each statement regarding an angle θ and its reference angle theta hat using radian measure. (Assume 0 ≤ θ < 2π. Give your answers in terms of θ.) (a) If θ is in QI, then theta hat = . (b) If θ is in QII, then theta hat = . (c) If θ is in QIII, then theta hat = . (d) If θ is in QIV, then theta hat = .
Answers
The reference angle is simply the acute angle between the terminal side and the x-axis
The terminal angles in the four quadrants are
[tex]\bar \theta = \theta[/tex].[tex]\bar \theta = \pi - \theta[/tex].[tex]\bar \theta = \theta - \pi[/tex].[tex]\bar \theta = 2\pi - \theta[/tex]The given parameters are:
[tex]\theta \to[/tex] reference angle
[tex]\bar \theta \to[/tex] terminal angle
(a) If the reference angle is in the first quadrant
In the first quadrant, the x-axis is at [tex]0\ rad[/tex]
So, the terminal angle is:
[tex]\bar \theta = \theta - 0[/tex]
[tex]\bar \theta = \theta[/tex]
(b) If the reference angle is in the second quadrant
In the second quadrant, the x-axis is at [tex]\pi \ rad[/tex],
While the reference angle is between [tex]\frac{\pi}{2}[/tex] and [tex]\pi \ rad[/tex]
It means that, we have to subtract the reference angle from the x-axis
So, the terminal angle is:
[tex]\bar \theta = \pi - \theta[/tex]
(c) If the reference angle is in the third quadrant
Here, the x-axis is still at [tex]\pi \ rad[/tex],
But the reference angle is between [tex]\pi \ rad[/tex] and [tex]\frac{3}{2}\pi[/tex]
It means that, we have to subtract the x-axis from the reference angle.
So, the terminal angle is:
[tex]\bar \theta = \theta - \pi[/tex]
(d) If the reference angle is in the fourth quadrant
Here, the x-axis is at [tex]2\pi \ rad[/tex]
And the reference angle is between [tex]\frac{3}{2}\pi[/tex] and [tex]2\pi \ rad[/tex]
It means that, we have to subtract the reference angle from the x-axis.
So, the terminal angle is:
[tex]\bar \theta = 2\pi - \theta[/tex]
See attachment for illustration of terminal angles
Read more about terminal angles at:
https://brainly.com/question/12891381
Final answer:
When dealing with angles in radians and their reference angles, each quadrant has a specific relationship for determining the reference angle based on the given angle θ.
Explanation:
Radian Measure with Reference Angles:
If θ is in QI, then θ hat = θ
If θ is in QII, then θ hat = π - θ
If θ is in QIII, then θ hat = θ - π
If θ is in QIV, then θ hat = 2π - θ
Related Questions
What is 100x100 I need help :(
Answers
The solution is, the value is 100 x 100 =10000.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
given that,
100 x 100
i.e. we have to multiply 100 with 100
so, we get,
100 x 100
=10000
Hence, The solution is, the value is 100 x 100 =10000
To learn more on multiplication click:
brainly.com/question/5992872
#SPJ5
The expression y2 – 10y + 24 has a factor of y – 4. What is another factor of y2 – 10y + 24? y – 20 y – 14 y – 8 y – 6
Answers
Answer:
(y-6)
Step-by-step explanation:
[tex]y^2 - 10y + 24[/tex]
We need to find out two factors whose product is 24 and sum is -10
-6 times -4 = 24
-6 + -4 = -10
So two factors are -6 and -4
We write the factors inside the parenthesis
(y-6) (y-4)
Factor (y-4) is already given
So another factor is (y-6)
Final Answer:
y - 6
Explanation:
To find another factor of the quadratic expression (y^2 – 10y + 24) given that (y – 4) is one factor, we need to perform factorization. Let's find the factors of the constant term, 24, which when added together give us the coefficient of the middle term, which is –10.
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24.
We are looking for two factors of 24 that add up to –10, and since one of the given factors is (y – 4), we are specifically looking for factors that would give us ((y - 4)) when multiplied by a binomial of the form (y - n), where (n) represents the other factor.
Now, notice that the factors 6 and 4 add up to 10, and when multiplying two binomial factors, we actually find such that when expanded they give us the original quadratic expression. In this case, (6 times 4 = 24), and (-6 + (-4) = -10), which are our constant and coefficient of \(y\), respectively.
Therefore, we can write the quadratic expression as the product of two binomial expressions: ((y - 6)(y - 4))
Since we are already given that \(y - 4\) is a factor, the other factor must be (y - 6).
True or False. If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
Answers
Answer:
True
Step-by-step explanation:
In simplest terms, if the triangle is ΔABC with ∠B≅∠C, then you can show ΔABC ≅ ΔACB using the ASA congruence theorem. (BC≅CB by the symmetric property). Then AB ≅ AC by CPCTC (corresponding parts of congruent triangles are congruent).
Gail ordered 5,675 pounds of flour for the bakery. The flour comes in 25-pound bags. How many bags of flour will the bakery receive?
Answers
227 bags is your answer
hope this helps
You originally draw a design for an art contest on a 4 in. x 5 in. card. The second phase of the contest requires the drawing to be transferred to an 8.5 in x 11 in. standard sheet of paper and utilize as much of the space on the paper as possible. You determine that the largest size one of the dimensions of your drawing can be is 10.5 in. What is the length of the other dimension if the two drawings are similar? Type your exact answer in the blank without the units, and round to the nearest tenths.
Answers
Answer:
x = 8.4
Explanation:
Red jeans inc. sells jeans that cost $16.55 for a selling price of $35.99. The percent of markup based on cost is
Answers
------------------- = 117.5 %
16.55
Answer:
Markup percent = 117.50%
Step-by-step explanation:
Markup percent = (sales price - unit cost)/unit cos *100
Given: Unit cost = $16.55, sales price = $35.99
Now plug in these given values in the above formula, we get
Markup percent = (35.99 - 16.55)/16.55 *100
= (19.44/16.55)*100
= 117.50%
Hope this will helpful.
Thank you.
Darius and Matthew have three fruit bars. They are both hungry after playing football and decide to split the fruit bars evenly.
Answers
How many solutions does 4x+8=2x+7+2x-20 have
Answers
Trey has answered 15 E-mails.This is 20% of E-mails he must answer.How many E-mails does he need to answer?
Answers
Find the general solution to y" + 2y' + 17y = 0
Answers
y'' + 2y' + 17y = 0
y(0) = 1 y'(0) = -1
Which answer shows these decimals written in order from greatest to least? 76.493 79.2 76.81 A. 79.2 > 76.493 > 76.81 B. 76.81 > 76.493 > 79.2 C. 79.2 > 76.81 > 76.493 D. 76.493 > 79.2 > 76.81
Answers
In a circle, a central angle whose measure is pi/2 radians intercepts an arc whose length is 3pi/2 centimeters. How many centimeters are in the radius of the circle?
Answers
the student council wants to rent a ballroom for the junior prom. the ballrooms rental rate $1500 for 3 h and $125 for each additional half hour. suppose the student council raises $2125. What is the maximum number of hours for which they can rent the ballroom
Answers
so the equation would be set up as
1500+125x= 2125
subtract 1500 from both sides and you should be left with
125x=625 divide 125 into both sides and you should get a answer of 5 then add the three hours and your final answer will be 8 hours is the maximum
Simplify three to the negative ninth divided by three to the negative twelfth.
Answers
Answer:
3^3
Step-by-step explanation:
What can you say about the continuous function that generated the following table of values?
Answers
Answer:
Option: B is the correct answer.
B. The function has more than one x-intercept.
Step-by-step explanation:
We are given a table of values as follows:
x y
-3 4
0 -3
1 2
5 0
11 7
As we know that a function is a continuous function this means that the graph first decreases from 4 to -3 ( since at x=-3 we have y=4 and at x=0 we have y= -3) and then it increases from -3 to 7 ( since at x=0 we have y= -3 and at x=11 we have y=7)
Hence, the function will intersect the x-axis two times between x= -3 and x=11.
Hence, the function has more than one x-intercept.
Answer: The function had more than in intercept,
Step-by-step explanation:
Write the percent as a fraction is lowest terms 65 1/2%
Answers
Work:
62.5%=62.5/100
=0.625
= 0.625/1 x 1000/1000
= 625/1000=5/8
deduct 20'x22' from 2240 total space?
Answers
To remove the area of 20'x22' from the total space of 2240 square feet, multiply the dimensions to get the area to deduct, which is 440 square feet. Then subtract this from the total area to find the remaining space, which is 1800 square feet.
Explanation:To deduct an area of 20 feet by 22 feet from a total space of 2240 square feet, you first need to calculate the area of the space you are removing. To find the area of a rectangle, you multiply its length by its width.
Area to deduct = Length × Width = 20' × 22' = 440 square feet.
Next, subtract the area to deduct from the total space:
Remaining space = Total space - Area to deduct = 2240 sq ft - 440 sq ft = 1800 square feet.
Therefore, you are left with 1800 square feet of space after deducting the area of 20'x22' from the original total space of 2240 square feet.
one of the models of a dinosaur used in filming of a movie was only 15in tall. In the movie, the dinosaur appeared to have an actual height of 20ft. What is the Scale of the model?
Answers
[tex]\bf \cfrac{model}{actual}\qquad 15:240\qquad \cfrac{15}{240}\implies \cfrac{1}{16}[/tex]
Brenda has a balance of d dollars in her piggy bank. Explain what value(s) d may have if d = 28
Answers
Brenda has a blance of 38 dollars in her piggy bank. What exactly do you still need to learn / know?
She might have 3-$10 bills, 1-$5 bill and 3-$1 bills. Other combinations are possible.
Use this equation to find dy/dx. 4y cos(x) = x2 + y2
Answers
don't worry about solving for y explicitly before differentiating.
(4y)cosx = x^2 + y^2
Apply product rule on the left,
and power rule on the right-hand terms,
(4y)'cosx + 4y(cosx)' = (x^2)' + (y^2)'
4y'cosx + 4y(-sinx) = 2x + 2yy'
4y'cosx - 4ysinx = 2x + 2yy'
Let's get both y' terms on the left side,
and everything else on the right,
4y'cosx -2yy' = 2x + 4ysinx
Factor y' out of each term,
y'(4cosx - 2y) = 2x + 4ysinx
Solve for y' (which is dy/dx) by dividing by the stuff,
y' = (2x + 4ysinx) / (4cosx - 2y)
You can divide a 2 out of everything to simplify it down a little bit.
y' = (x + 2ysinx) / (2cosx - y)
Samuel filled the glasses shown below completely with water. The total amount of water that Samuel poured into the glasses is 60 cubic centimeters. What is the height of glass 1? Round your answer to the nearest tenth. (Use π = 3.14.) Note that all measurements are in centimeters and images are not drawn to scale.
The possible answers are 0.2, 1.7, 3.9 or 5.6. When googled the answer always comes up 3.9. I always get 1.6527 which rounds up to 1.7. How about you?
Answers
volume of glass 2 = pi*r^2*h/3= 3.14 *2.5^2*6/3 = 39.25 cubic cm
60-39.25 = 20.75 cu cm was in 1st cup
volume of cylinder = pi *r^2 *h
20.75 = 3.14 *2^2 *h
20.75 = 3.14*4*h
20.75 = 12.56*h
h = 20.75 /12.56 = 1.652 round to 1.7
Answer:
The height of glass 1 is 1.7 cm.
Step-by-step explanation:
We are given the following information in the question:
The total amount of water that Samuel poured into the glasses is 60 cubic centimeters.
Volume of glass 2 = Volume of cone =
[tex]\displaystyle\frac{1}{3}\pi r^2h\\\\\text{Putting value of r and h}\\\\= \frac{1}{3}\times 3.14\times \frac{5}{2}\times \frac{5}{2}\times 6 = 39.25\text{ cubic cm}[/tex]
Volume of glass 1 =
[tex]\text{ Total Volume } - \text{Volume of glass 2}\\= 60 - 39.25\\= 20.75\text{ cubic cm}[/tex]
Volume of glass 1 = Volume of cylinder =
[tex]20.75 = \pi r^2h\\\text{where r is the radius of cylinder and h is the height of cylinder}\\\\\text{Putting the values of r}\\\\ 20.75 = 3.14\times \displaystyle\frac{4}{2}\times \frac{4}{2}\times h\\\\h = \frac{20.75}{3.14\times 2\times 2} 1.656 \approx 1.7[/tex]
Thus, the height of glass 1 is 1.7 cm.
If $6000 is invested at 7% simple interest for 4 months, how much interest is earned?
Answers
S = Prt
S = Simple Interest
P = Principle = 6000
r = rate = 7% = .07
t = time = 4
S = 6000 * .07 * 4
S = $1680
A grade has 81 girls and 72 boys. The grade is split into groups that have the same ratio of girls to boys as the whole grade. How many girls are in a group that has 16 boys?
Answers
For the given function sin−1(9x + 1), the "inside" function is 9x + 1 and the "outside" function is
Answers
In the function sin⁻¹(9x + 1), the 'outside' function is sin⁻¹(x). This is because it is the function performing an operation on the 'inside' function, which is 9x + 1.
Explanation:For the function sin−1(9x + 1), the 'inside' function is indeed 9x + 1. The 'outside' function is sin⁻¹(x), also known as the inverse sine or arcsine function. In composite functions, the 'inside' function is the function that is being acted on, while the 'outside' function is the function carrying out the action on the inside function. So here, the action of sine inverse or arcsine is being performed on the 'inside' function 9x + 1.
Learn more about Composite Functions here:https://brainly.com/question/30143914
#SPJ12
The sales tax rate on camping equipment is 7 percent. Olivia will buy a sleeping bag priced at $35.35 and a tent at $52.75. What amount will Olivia spend on the sales tax.
Answers
F(x)=5(3-x)^2 what is f(-4)
Answers
f(x) = 5(3-x)^2
f(x) = 5*(3-x)^2
f(-4) = 5*(3-(-4))^2 ... replace every x with -4
f(-4) = 5*(3+4)^2
f(-4) = 5*(7)^2
f(-4) = 5*(49)
f(-4) = 245
-----------------------------------------
Final Answer: 245
what is the value of-3 2/3÷1/3
Answers
[tex]\bf \stackrel{mixed}{3\frac{2}{3}}\implies \cfrac{3\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{11}{3}}\\\\ -------------------------------\\\\ \cfrac{3\frac{2}{3}}{\frac{1}{3}}\implies \cfrac{\quad \frac{11}{3}\quad }{\frac{1}{3}}\implies \cfrac{11}{3}\cdot \cfrac{3}{1}\implies \cfrac{33}{3}\implies 11[/tex]
What is the sum and classification of 3/20 + sqrt of 10
A. 3.31227766..., irrational
B. 3.31227766..., rational
C.18.16227766..., irrational
D.18.16227766..., rational
Answers
Answer:
a
Step-by-step explanation:
Answer:
A. 3.31227766..., irrational
Step-by-step explanation:
We have been given two numbers. We are asked to find sum of given numbers and classify the type of number after addition.
[tex]\frac{3}{20}+\sqrt{10}[/tex]
[tex]0.15+3.1622776601683793[/tex]
[tex]3.3122776601683793[/tex]
We can see that [tex]\frac{3}{20}[/tex] is a rational number, while [tex]\sqrt{10}[/tex] is an irrational number as its digits are repeating infinitely after decimal.
We know that sum of a rational and irrational number is irrational, therefore the sum of given numbers is irrational and option A is the correct choice.
Julian is mixing drops of food coloring to create green frosting for a cake. He uses 18 drops of yellow dye and 12 drops of blue dye. Find the ratio of drops of blue dye to total drops of dye. Express as a simplified ratio.
Answers
Answer:
The ratio would be 2:5
Explanation:
The ratio of drops of blue dye to total drops of dye is got by dividing drops of blue dye (12) by total drops, which is the sum of blue and yellow drops (12+18):
[tex]\displaystyle\frac{12}{12+18}=\frac{12}{30}[/tex]
Once we simplify the fraction by dividing both top and bottom by 6, we would get:
[tex]\displaystyle\frac{2}{5}[/tex]
Therefore, the ratio of drops of blue dye to total drops of dye is: 2:5
The simplified ratio of blue dye to total dye used by Julian is 2:5. This means that for every 2 drops of blue dye, there are 5 total drops of dye.
Explanation:The question is asking for the ratio of blue dye to the total amount of dye. Julian used 12 drops of blue dye and 18 drops of yellow dye, making the total number of dye drops 30 (12 blue + 18 yellow). Therefore, the ratio of blue dye to total dye is 12 to 30. However, this ratio can be simplified by dividing each figure by their greatest common divisor (gcd) which is 6. So, the simplified ratio is 2:5.
This means for every 2 drops of blue dye, there are 5 total drops of dye. It's a useful way of comparing quantities in mathematics or in everyday life circumstances like this one, where Julian is mixing dyes.
Learn more about Ratios here:https://brainly.com/question/32531170
#SPJ3
Please help me with this question on algebra
Answers
0 4
- 6 1
3 -4
Rember rows times columns.
=>
a11 = 4*0 + 0*(-3) = 0
a12 = 4*1 + 0*1 = 4 + 0 = 4
a21 = -1*0 + 2*(-3) = 0 - 6 = -6
a22 = -1*1 + 2*1 = -1 + 2 = 1
a31 = -3*0 + (-1)*(-3) = 0 + 3 = 3
a32 = -3*1 + (-1)*1 = -3 - 1 = -4