Answers
Check the picture.
For the moment let [tex]\displaystyle{ \cos\theta= \frac{8}{17} [/tex] (we make it positive since we are modeling using a triangle.)
Using the Pythagorean theorem, the length of the side opposite to angle [tex]\theta[/tex] is found to be 15 units.
We can see that the sine of theta is [tex]\displaystyle{ \sin\theta= \frac{opposite \ side}{hypotenuse}= \frac{15}{17} [/tex].
In the third quadrant, both sine and cosine of an angle are negative, so the actual values of the sine and cosine of theta are, eventually:
[tex]\displaystyle{ \sin\theta=- \frac{15}{17} [/tex], [tex]\displaystyle{ \cos\theta=- \frac{8}{17} [/tex].
Recall the double-angle identities (formulas):
[tex]\sin 2\theta=2\sin\theta\cos\theta[/tex], [tex]\cos2\theta=cos^2(\theta)-sin^2(\theta)[/tex].
Using these identities and the ratios found above, we have:
[tex]\displaystyle{ \cos2\theta=cos^2(\theta)-sin^2(\theta)=(- \frac{8}{17})^2-(- \frac{15}{17})^2=\frac{64}{289}-\frac{225}{289}=\frac{-161}{289}[/tex]
Similarly, applying the double angle formula for the sine we have:
[tex]\displaystyle{ \sin 2\theta=2\sin\theta\cos\theta=2\cdot(- \frac{8}{17})(- \frac{15}{17})=\frac{240}{289}[/tex]
[tex]\displaystyle{ \tan2\theta= \frac{\sin 2\theta}{\cos 2\theta}= \frac{\frac{240}{289}}{\frac{-161}{289}}= -\frac{240}{161} [/tex]
Answer:
[tex]\displaystyle{\cos2\theta=\frac{-161}{289}[/tex]
[tex]\displaystyle{ \tan2\theta= -\frac{240}{161}[/tex]
Related Questions
Evaluate log64 + 2log5 - 2log40
Answers
The table below shows the number of pencils of different colors in a box:
Color of Pencil Number
Purple 10
Blue 1
Yellow 6
Pink 3
Pam draws a color pencil from the box randomly without looking. What is the probability that Pam will select a yellow pencil and the coin will land tails up?
2 over 40
6 over 40
12 over 20
16 over 20
Answers
Answer:
6 over 40
Step-by-step explanation:
6/40 or 3/20 is the probability that Pam will select a yellow pencil and the coin will land tails up.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given that, The table below shows the number of pencils of different colors in a box:
Color of Pencil Number
Purple 10
Blue 1
Yellow 6
Pink 3
From the general formula of probability:
Probability = (desired outcome)/ (Total outcome)
In our case
Total outcomes = (number of pencils) * (coin sides)
Total outcomes = 20 * 2
Total outcomes = 40
Desired outcomes = Pam will select a yellow pencil and the coin will land tails up
Desired outcome = (number of yellow pencils) * (coin sides)
Desired outcome = 6 * 1 = 6
Thus,
Probability = 6/40
therefore, the probability that Pam will select a yellow pencil and the coin will land tails up is 6/40 or 3/20.
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A package of 5 pairs of insulated gloves costs 29.45 what is the cost of a single glove?
Answers
If the entire pack cost $29.45, we divide that by 10 to determine the cost of a single glove:
$29.45 ÷ 10 = $2.945 which rounds to $2.95 per glove.
Given that the package contains 5 pairs of gloves
Let us first establish some facts
We know that a pairs consist of 2 glovesIn all we have 10 glovesNow let us solve for the cost of a glove
if 10 gloves cost 29.45
the 1 glove will cost x
Cross multiply to solve for x
10*x = 1*29.45
divide both sides by 10
x = 29.45/10
x= 2.945
Hence the cost of a single glove is 2.945
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Which expression is equivalent to −4.5+(−5.5)+(−3.1) ?
1. (4.5+5.5)+(−3.1)
2. −4.5+(5.5+3.1)
3. −(4.5+5.5+3.1)
4. −4.5−(5.5−3.1)
Answers
Answer:
i think the answer is also A
Step-by-step explanation:
find the equation of the line that contains the point (-1,-11) and is parallel to the line 7x+3y=10
Answers
To find the equation of a line, you need two things: the slope and the y-intercept.
The slopes of parallel lines are the same. So we can find the slope of the new line by finding the slope of the first line. To do that, we need to put it in y=mx+b format, where m is the slope. So we must rearrange the 7x+3y=10. First subtract 7x from both sides to make it look like:
[tex]3y=10-7x[/tex]
Then divide both sides three:
b[tex]y= \frac{10}{3} - \frac{7}{3} x[/tex]
So now that it's in y=mx+b format, we can now see that the m= - \frac{7}{3}
Now we know the m of the new equation, we need to find the b, or the y-intercept. To do this, we can plug the point we have and the m value into the y=mx+b format.
[tex](-11)=- \frac{-7}{3} (-1) + b[/tex]
Solving this, we can subtract 7/3 from both sides:
[tex]-11- \frac{7}{3} = b[/tex]
Therefore, b= [tex]-13 \frac{1}{3} [/tex]
Plugging the m= - \frac{7}{3} and the b= [tex]-13 \frac{1}{3} [/tex] back into the y=mx+b format, your parallel line is y=- \frac{7}{3} [tex]-13 \frac{1}{3} [/tex].
A flower shop received a total of 24 boxes of roses each box had red yellow and white roses there were 16 in each box the shop receive a total of 125 red roses and 112 yellow roses how many white rose to the shop receive
Answers
Ella and Margaret were at a carnival. They each got a ticket to the Ferris wheel. Ella got a snow cone, and Margaret got a cotton candy. Ella had a certificate for $6 off the cost. Margaret paid the rest, which came to $12.75. Each Ferris wheel ticket is $5. And a snow cone is $3.50. What was the cost of the cotton candy? A.$5.00 B.$5.25 C.$2.50 D.$7.25
Answers
Answer:
B.$5.25
Explanation:
There were 2 tickets to the Ferris wheel; each is $5. This can be written as 2(5).
Ella got a snow cone, which cost $3.50. This gives us 2(5) + 3.50.
Margaret got a cotton candy, the cost being unknown; this gives us 2(5)+3.50+x.
Ella had a certificate for $6 off the cost; this gives us 2(5)+3.50+x-6.
This makes the equation
2(5)+3.50+x-6=12.75
Combining like terms, we have
7.50+x = 12.75
Subtract 7.50 from each side:
7.50+x-7.50 = 12.75 - 7.50
x = 5.25
−13−(−12)
A number line ranging from negative one to one with an arrow on both ends and tick marks every one third
−16
0
16
12
Answers
Answer:
Option C.
Step-by-step explanation:
The given expression is
[tex]-\frac{1}{3}-(-\frac{1}{2})[/tex]
We know that (-)(-)=(+). So, the given expression can be written as
[tex]-\frac{1}{3}+\frac{1}{2}[/tex]
Taking LCM we get
[tex]\frac{-2+3}{3\times 2}[/tex]
[tex]\frac{1}{6}[/tex]
The value of given expression is 1/6.
Two numbers are [tex]-\frac{1}{3}\text{ and }-\frac{1}{2}[/tex]. Mark these point on the given number number.
Now, move from [tex]-\frac{1}{2}[/tex] to [tex]-\frac{1}{3}[/tex] and count the number of jumps.
Number of jumps from [tex]-\frac{1}{2}[/tex] to [tex]-\frac{1}{3}[/tex] is 1.
1 Jump = 1/6
Therefore, the value of given expression is 1/6, therefore the correct option is C.
Alejandro and Pedro are riding their bike to school. After 1 mile, the are 5/8 of the way there. How much farther do they have to go?
Answers
cross multiply
5/8x = 1
x = 1 / (5/8)
x = 1 * 8/5
x = 8/5 or 1 3/5 miles...total distance
and if they already rode 1 mile.....(1 3/5 - 1) = 3/5 of a mile left to go <==
Convert: 2°C to °F (to the nearest tenth).
Answers
1) Tf = 9/5(2) + 32
2) Tf = 3.6 + 32
3) Temperature of farenheit = 35.6
5c-15 factor out the coefficient of the variable
Answers
To factor out the coefficient of the variable from 5c - 15, divide both terms by the coefficient which is 5, yielding the factored form: 5(c - 3).
Explanation:The expression 5c - 15 involves multiplication by the coefficient of the variable c and subtraction of 15. To factor out the coefficient of the variable here, we're looking to take out a common factor from both 5c and -15. The coefficient of the variable c is 5, which is also a factor of -15.
So, to factor out the coefficient of the variable (which is 5) we divide both terms by 5, which gives us: 5(c - 3). Here, 5 is factored out and (c - 3) is what remains.
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Jennifer uses the formula P = 0.5e - 5 to determine the profit (P) she makes from selling any number of erasers (e). Last week Jennifer had a profit of $63. How many erasers did Jennifer sell?
Answers
Answer:
136
Step-by-step explanation:
did the interim (usatestprep)
How long does it take each horse to run a mile
Answers
The correct answer is;
Horse A will take 4 minutes to run 1 miles, while horse B will take 2 minutes 30 seconds to run 1 mile.
Analysing the graph, the Distance is measured in miles, while the Time is measured in minutes.
For horse A, the time taken to run 1 miles is 4 minutes, according to the graph.
For horse B, the time taken to run 1 mile is 2 minutes 30 seconds according to the graph.
Therefore, according to the graph, it will take horse A and horse B, 4 minutes and 2 minutes 30 seconds respectively, to run a mile.
what is the value of the 2 in 54.625
Answers
-11.3 is rational or irrational ? explain? 0.083 and 2.1371938 to please if its not much to ask?
Answers
------- = ----------
1 10
Since this is the ratio of two integers, 11.3 is rational. So is 11.3.
83
If you really mean 0.083, this is rational: it is ---------
1000
If y ou meant 0.083333333 ... , that's also rational: 1/12 is equivalent.
a line contains the points (82,-96) and (87,-86)
what is the sloped line is simplified form?
Answers
Let's label the points. (82[x1], -96[y1]) (87[x2], -86[y2])
-86 - -96 would turn into -86 + 96, coming out to 10.
87 - 82 = 5.
10/5 would be the unsimplified slope.
Divide both numbers by 5, and you get 2/1.
2/1 simplifies to 2 because two divided by one equals two, as one can go into two twice.
Slope line in simlified form: 2
Answer:
2
Step-by-step explanation:
How do you write 26/10 as a percentage
Answers
The way we explain this is you multiply 26 * 10 and 10 * 10. You get 260/100.
260/ 100 as a percentage is 260%.
Which is bigger 7/8 or 0.78
Answers
78/100
Simplified it is: 39/50
So, now you cross multiply 7/8 and 39/50 to check it. The number is larger over the 7/8 so you know it is greater.
So, in conclusion 7/8 > 0.78
I hope this helps:)
Which sentence illustrates the commutative property of addition?
Answers
7+8+9=24 so 8+7+9 also equals 24. commutative property is just switching the order that the numbers appear in but in the end, still equals the same thing
the marching band is having a show to raise at least $1000 forntheir upcoming trip. Each adults is $6 and students $4. The auditorium has a maxium capacity of 200 people.
Answers
Let a = adult
Let s = student
6a + 4s = 1000...A
a + s = 200...B
We have a system of linear equations in two variables, the variables a and s.
You can select any variable of choice to represent the adults and students.
Solve equation B for a or s (your choice).
a + s = 200
Solve for a or s (your choice).
s = 200 - a
Plug into equation A to find the value of a.
6a + 4(200 - a) = 1000
6a + 800 - 4a = 1000
6a - 4a = 1000 - 800
2a = 200
a = 200/2
a = 100
There are 100 adults.
Plug a = 100 into EITHER equation A or B to find students.
a + s = 200
100 + s = 200
s = 200 - 100
s = 100
There are also 100 students.
Did you follow?
if five is subtracted from three times a certain number,the result is 10.what is the number?
Answers
3n - 5 = 10.
Next, isolate the variable.
3n - 5 = 10
+ 5 + 5
3n = 15
Lastly, solve for n.
3n/3 = 15/3
n = 5
(a − 6)2
Find the product. (Simplify your answer completely.)
Answers
(a - 6)2
Multiply each term in the parenthesis by 2
2a - 6 × 2
Multiply the numbers
Your answer is
2a - 12
I'm going to move the 2 onto the other side, because it's easier for me to visually do :)
2(a - 6)
Simplify.
(2 × a) + (2 × -6)
Simplify.
2a + -12
2a - 12
~Hope I helped!~
4.5(8-x)+36=102-2.5(3x+24) show step by step how to solve please.
Answers
Combine like terms: 36 + 36 = 72 72 + -4.5x = 102 + -2.5(3x + 24)
Reorder the terms: 72 + -4.5x = 102 + -2.5(24 + 3x) 72 + -4.5x = 102 + (24 * -2.5 + 3x * -2.5) 72 + -4.5x = 102 + (-60 + -7.5x)
Combine like terms: 102 + -60 = 42 72 + -4.5x = 42 + -7.5x Solving 72 + -4.5x = 42 + -7.5x Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '7.5x' to each side of the equation. 72 + -4.5x + 7.5x = 42 + -7.5x + 7.5x
Combine like terms: -4.5x + 7.5x = 3x 72 + 3x = 42 + -7.5x + 7.5x
Combine like terms: -7.5x + 7.5x = 0.0 72 + 3x = 42 + 0.0 72 + 3x = 42
Add '-72' to each side of the equation. 72 + -72 + 3x = 42 + -72
Combine like terms: 72 + -72 = 0 0 + 3x = 42 + -72 3x = 42 + -72
Combine like terms: 42 + -72 = -30 3x = -30
Divide each side by '3'. x = -10
Simplifying x = -10
a circle with a 12 in diameter is folded in half and folded again whats the area of the resulting shape
PLEASE HELP!!!!!!1
Answers
Can you please help me with #7&8 thanks in advance
Answers
Let B = fraction of the bulletin board
for Homeroom 101
B = (3/5)(1/2)
B = 3/10
Given a right triangle, find the degree measure of the angles if one angle is ten degrees more than four times the degree measure of the other angle and the third angle is the right angle.
Answers
a right angle is 90 degrees
the other 2 angles must equal 180-90 = 90 degrees
1st angle = x
2nd angle = 4x+10
add them together:
x + 4x +10 = 90
combine like terms:
5x +10 = 90
subtract 10 from each side:
5x =80
divide both sides by 5:
x = 80 /5 = 16
1st angle = 16 degrees
2nd angle = 4(16) +10 = 64 +10 = 74 degrees
Carol’s car seats one third the number of people that Joan’s car can seat. Two people can be seated in Carol’s car. How many people can Joan’s car seat?
Answers
Harvey needs to raise $400 he has 100 books to sell at $8.00 each what inequality shows this
Answers
x ≥ 100
these are the inequalities you need, first find x, then plug x in to top inequality
hope this helps
Please explain how to do this
Answers
so the margin will be (10-5 1/2)/2.
graph y = 1/2 x - 3
PLS HELP !!!