What is the value of cos(x/2) if tan x=1/2 and x is in quadrant III
Answers
Answer:
Step-by-step explanation:
The value of cos(x/2) is required.
The required value is [tex]\cos(x/2)=-\sqrt{\dfrac{5-2\sqrt{5}}{10}}[/tex]
TrigonometryThe given value is
[tex]\tan x=\dfrac{1}{2}[/tex] where x is in quadrant III.
From trigonometric identities we have
[tex]\sec^2x=1+\tan^2x\\\Rightarrow \sec^2x=1+(\dfrac{1}{2})^2\\\Rightarrow \sec^2x=\dfrac{5}{4}\\\Rightarrow \cos^{2}x=\dfrac{4}{5}\\\Rightarrow \cos x=\dfrac{2}{\sqrt{5}}[/tex]
If x lies in quadrant III then x/2 lies in quadrant II.
Cos is negative in quadrant III so,
[tex]\cos x=-\dfrac{2}{\sqrt{5}}=-\dfrac{2\sqrt{5}}{5}[/tex]
[tex]\cos \dfrac{x}{2}=\pm \sqrt{\dfrac{1+\cos x}{2}}\\ =\pm\sqrt{\dfrac{1-\dfrac{2\sqrt{5}}{5}}{2}}\\ =\pm\sqrt{\dfrac{5-2\sqrt{5}}{10}}[/tex]
Since, x/2 lies in the second quadrant and cos (x/2) is negative.
The required value is [tex]-\sqrt{\dfrac{5-2\sqrt{5}}{10}}[/tex]
Learn more about trigonometry:
https://brainly.com/question/24349828
Related Questions
What is the solution for the
equation x+1 = x+2?
Answers
Answer:
nosoulutions
Step-by-step explanation:
Answer:
There are no solutions.
Step-by-step explanation:
Jonathan and his band want to record and sell CDs. The recording studio charges an initial set-‐up fee of $250, and it charges $6.00 to burn each CD. define the variabvles in this situation
Answers
Plssss help meeee!!!
Answers
Answer:
The Answer is C
Step-by-step explanation:
To simplify the expression you will simply need to take the -7 and multiply it by each of the exponents. -7 times -3=21 and -7 times 3=-21
Hope this helps.
A circle has its centre at the origin and has equation
x + y = 81
What is the size of the radius?
Answers
Answer:
radius = 9
Step-by-step explanation:
The equation of the circle centred at the origin is
x² + y² = r² ( where r is the radius )
Given
x² + y² = 81, then
r² = 81 ( take the square root of both sides )
r = [tex]\sqrt{81}[/tex] = 9
teresa purchased a prepaid phone card for $30. Long distance calls cost 7 cents a minute using this card. Teresa used her card only once to make a long distance call. if the remaining credit on her card is $28.32, how many minutes did her call last?
Answers
Answer:
24min
Step-by-step explanation:
30-28.32=1.68
1.68/0.07cents=24
Please help due in a hour!!
Answers
Answer:
f(x)=1/2(x-4)^2+2
find the equation of the line.
use exact numbers.
y=__x+__
Answers
Answer:
[tex]y = -\frac{3}{2}x+ 3[/tex]
Step-by-step explanation:
Kailey correctly graphed the opposite of –3.3 on the number line.
A number line going from negative 5 to positive 5. Point A is between negative 4 and negative 3, point B is between negative 3 and negative 2, point C is at 3.3, and point D is at 3.9.
Which point could be the point Kailey graphed?
Answers
The number line shows that Kailey could have graphed the point C (3.3).
Number LineThe number line is the graphic representation of real numbers whose center is represented by the number zero (0). The negative numbers are on the left side of the number line, on the other hand, the positive numbers are written on the right side. See the attached image.
Opposite NumbersOpposite numbers are numbers that the distance to 0 is equal. The numbers are classified as the opposite when the sum between them is equal to zero (0).
STEP 1 - Plot the number linePlot the number line with the given limits: -5 to 5. See the attached image.
STEP 2 - Plot the given points in the number linePlot the points A, B,C an D in the number line drawn in step 1. See the attached image.
STEP 3 - Analyse the plotted number lineLike the point graphed is the opposite of -3.3, Kailey could have plotted the point C which is at 3.3 since the sum between -3.3 and 3.3 is equal to zero (0).
-3.3+3.3 =0
Read more about opposite numbers here:
https://brainly.com/question/13114728
#SPJ2
How would you graph the result of -3 + 5 as a point on the number line?
two places to the right of zero
two places to the left of zero
eight places to the right of zero
eight places to the left of zero
Answers
Angel bought a plant and planted it in a pot near a window in his house. The plant grew at a rate of 3 inches per month and its height at the time of purchase was 15 inches. Write an equation for
H
,
H, in terms of
t
,
t, representing the height, in inches, of the plant
t
t months after Angel bought the plant.
Answers
H = 15 + 3t, is the equation representing the height, in inches, of the plant tt months after Angel bought the plant.
What is an equation?Equation is a mathematical and physical statement that describes physical occurrences and the relationship between various physical quantities. It usually consists of basic variables that show physical quantities, but it may also point to a personal variable like your energy.
An equation that has a "equal to sign (=)" either reveals the answer or represents the value of the variable. However, since there is no equal sign in the case of an expression, there can be no clear answer and the value of the concerned variable cannot be displayed.
Given that,
H representing the height, in inches, of the plant
t months after Angel bought the plant
Thus, equation becomes: H = 15 + 3t
To know more about equation refer to:
brainly.com/question/14107099
#SPJ1
The sum of 324 and 135 is 503. Which number base was used for this calculation.
Answers
Answer:
Base 6 was used
Step-by-step explanation:
Here, we want to find which number base was used for the addition calculation
We start by adding the two end numbers
4 + 5 = 9
But 3 was recorded;
That means we can have 6 as the number base( 9/6 = 1 r 3)
We still continue to verify this;
The next addition is 2+3 = 5, adding the 1 brought forward, we have 6, but 0 was recorded
6/6 is (1 r 0)
This still further corroborated the earlier assertion;
then lastly 3 + 1 + 1 (1 brought forward); 5
This was recorded directly to show that the base in question is not less than 5
Hence our base of addition is base 6
give an example of a rational number
Answers
17
0.80
-22
Solve for y.
4(y - 8) + 6 = 58
Answers
Answer:
[tex]4(y - 8) + 6 = 58 \\ or \: 4y - 32 + 6 = 58 \\ or \: 4y - 26 = 58 \\ or \: 4y = 58 + 26 \\ or \: 4y = 84 \\ or \: y = \frac{84}{4} \\ or \: y = 21[/tex]
21 is the answer.....Hopes to get BRAINLIEST......Hopes it helps you.......Thank you ☺️
13.El área de un terreno rectangular es de 24 m2. Si el largo mide 2 m más que el ancho. A=24 m2 a) ¿Qué ecuación cuadrática resuelve el problema? b) ¿Cuáles son sus dimensiones? Largo= Ancho=
Answers
Answer:
Area = L · A = 24 m²
L = A + 2
reemplazamos:
(A + 2) · A = 24
A² + 2A - 24 = 0 ⇒ esta es la ecuacion quadratica
la solucion es: (A + 6) · (A - 4)
largo = 6 metros
ancho = 4 metros
three fourth c = five ninthe
Answers
Answer:
Step-by-step explanation:
3/4c=5/9
C=5×4/9×3
C=20/27
There are 92,746 seats available for fans at UGA's Sanford Stadium. Auburn University's Jordan-Hare Stadium has seating for 87,451 for fans. How many more seats are there at UGA's stadium?
Answers
Given :
Number of seats at UGA's Sanford Stadium, [tex]n_1 = 92,746[/tex] .
Number of seats at Auburn University's Jordan-Hare Stadium, [tex]n_2=87,451[/tex] .
To Find :
How many more seats are there at UGA's stadium.
Solution :
Extra seats at UGA's stadium = seats at UGA's Sanford Stadium - seats at
Auburn University's Jordan-Hare Stadium
= 92,746 - 87,451
= 5295
Hence, this is the required solution.
Marlon earned $8.50 per hour plus an additional $80 in tips waiting tables on Saturday. He earned at least $131 in all. If h represents the number of hours Marlon worked, which inequality represents the minimum number of hours, to the nearest hour, that Marlon worked on Saturday?
Question 1 options:
8h + 80 ≥131
80h + 8.50 ≥ 131
8.50h + 80 ≤ 131
80h + 8.50≤ 131
Answers
Answer:
8.50h + 80 ≥131Step-by-step explanation:
The answer is not in the option
Step one:
given data:
we are told that the hourly earning= $8.50
then additional tip=$80
total earnings=$131.
Step two:
the linear function for the total earning is the same as the equation of a line
y=mx+c
where
y represents the total earning of $131
m represents the hourly earning= $8.50
x represents the number of hours h
c represents the tip of $80
The expression for the situation is modeled as
8.50h + 80 ≥131Golf balls come in a variety of packages. A particular brand of golf balls come in packages of 12 or in packages of 18. The 12-pack costs $4.47 and the 18-pack costs $14.46. Which is the better deal and what is the unit price of the better deal?
Answers
Answer:
The better deal is the 12 pack because the unit price is $0.37 which is lower than the unit price of the 18 pack that is $0.80.
Step-by-step explanation:
To find which is the better deal, you have to determine which one offers a lower unit price by dividing the price of each package by the number of balls in the pack:
$4.47/12=$0.37
$14.46/18=$0.80
According to this, the answer is that the better deal is the 12 pack because the unit price is $0.37 which is lower than the unit price of the 18 pack that is $0.80.
solve the equation 4x²+4x+1=0
Answers
Answer: x = -1/2
4x² + 4x + 1 = 0
⇔ (2x + 1)² = 0
⇒ 2x + 1 = 0
⇔ x = -1/2
Step-by-step explanation:
A dripping faucet leaks 3 ounces of water each minute. How many ounces of water leak in 2 hours and 15 minutes?
Answers
Answer:
405 ounces of water
Step-by-step explanation:
1 hr = 60 mins
2hrs= 120 mins (60 x 2)
120 + 15 = 135
135 x 3 = 405
Answer:
the answer is 1.875 gallons
Step-by-step explanation:
pls answer this One way to solve an equation or inequality that has both decimals and fractions is to change the
fractions to decimals. What is another way to solve an equation or inequality that has both fractions and
decimals?
Answers
Answer:
Turn everything into fractions. You can also combine like terms.
Step-by-step explanation:
Complete the statement, then write the postulate you used.
Please help! I’ll give brainliest!
Answers
Mallory records the number of hours she spends babysitting and the amounts of money she is paid. What is the constant rate of proportionality between the number of hours Mallory babysits and the amount of money she is paid, in dollars?
Please explain as well, I do not understand how I would find the answer.
Answers
Answer:
Mallory gets paid $20 for every 1 hour.
Step-by-step explanation:
You take the lowest set of numbers in this table, & divide them to find how much it would be for 1 hour: $40÷2hours= $20
ratio 1 hr./20 dollars
PLZ HELP 20 POINTS I REALLY NEED THIS KKKJHGKJHGKJHGKJHGKJHG
Answers
Can someone please please help me. ?????
Answers
Answer:
#1
x intercept is -5
y intercept is -5
#2
y=8x
Step-by-step explanation:
can someone help please ill give brainlyest if right
Answers
Then according to the above statement, we have the following equation:-
[tex]3 + 4x = 6x - 5[/tex]
Subtract 4x from both sides , we get
[tex]3 = 2x - 5[/tex]
Add 5 on both the sides , we get
[tex]8 = 2x[/tex]
Divide both sides by 2 , we get
[tex]4 = x[/tex]
Hence, the number is 4
1.15÷0.23=? pls answer guys
Answers
Answer:
5
Step-by-step explanation: I used a calculator
How much will you get paid if you work 28.5 hours for $7.75 per hour?
Answers
Answer:
$220.87 but 220.88 if u have to round up :)
$220.875
Explanation:
If it is $7.75 dollars an hours and you want to know much much you will make you will multiple how many hours with the amount.
$7.75 x $28.5
PLZZZ HELP ME 10 PTSS
What is the product of -3 1/3and -8 7/10?
A. 9/5
B. 2
C. 275/30
D. 29
Answers
Answer:
5 31/ 30 or 6 1/30
Step-by-step explanation:
I wish this helped you
Answer:
D. 29
Step-by-step explanation:
First, let's make things a bit easier for ourselves and convert mixed numbers to improper fractions
[tex]-\frac{10}{3}* -\frac{87}{10}[/tex]
Next, we check for numbers that can cancel out. In this case, we have 10.
[tex]-\frac{1}{3}*-\frac{87}{1}[/tex]
Because negatives cancel out, we get
[tex]\frac{87}{3}[/tex]
when we multiply.
Fractions just mean division, so we divide 87 by 3 and get
D. 29
The function P(x) = –0.015x^2 + 1.2x – 11.5 gives the profit, in thousands of dollars, when a company sells a new product at x dollars per unit. Which of the following statements best interprets the average rate of change of this function from x = 50 to x = 55?
The profit increases by $375 for every $1 increase in the selling price.
The profit decreases by $375 for every $1 increase in the selling price.
The profit increases by $1875 for every $1 increase in the selling price.
The profit decreases by $1875 for every $1 increase in the selling price.
Answers
Answer:
The profit decreases by $ 375 for every $ 1 increase in the selling price.
Step-by-step explanation:
From the definition of the secant line we get that the average rate of change of [tex]P(x) = -0.015\cdot x^{2}+1.2\cdot x -11.5[/tex], where [tex]x[/tex] is the selling price of the product, measured in dollars per unit, is:
[tex]r = \frac{P(55)-P(50)}{55-50}[/tex] (1)
Now we evaluate the function at each bound:
x = 50
[tex]P(50) = -0.015\cdot (50)^{2}+1.2\cdot (50)-11.5[/tex]
[tex]P(50) = 11[/tex]
x = 55
[tex]P(55) = -0.015\cdot (55)^{2}+1.2\cdot (55)-11.5[/tex]
[tex]P(55) = 9.125[/tex]
Then, the average rate of change is:
[tex]r = \frac{9.125-11}{55-50}[/tex]
[tex]r = -0.375[/tex]
Hence, the profit decreases by $ 375 for every $ 1 increase in the selling price.
The statements that best interprets the average rate of change from x = 50 to x = 55 is (b) The profit decreases by $375 for every $1 increase in the selling price.
The profit function is given as:
[tex]P(x) = -0.015x^2 + 1.2x - 11.5[/tex]
Calculate P(x), when x = 50.
So, we have:
[tex]P(50) = -0.015(50)^2 + 1.2(50) - 11.5[/tex]
[tex]P(50) = 11[/tex]
Calculate P(x), when x = 55.
So, we have:
[tex]P(55) = -0.015(55)^2 + 1.2(55) - 11.5[/tex]
[tex]P(55) = 9.125[/tex]
The average rate of change from x = 50, to 55 is then calculated using:
[tex]m = \frac{P(55) - P(50)}{55-50}[/tex]
So, we have:
[tex]m = \frac{9.125 - 11}{55-50}[/tex]
[tex]m = \frac{-1.875}{5}[/tex]
Divide
[tex]m = -0.375[/tex]
The function is in 1000 units.
So, we have:
[tex]m = -0.375\times 1000[/tex]
[tex]m = -375[/tex]
-375 implies a decrease of $375 for every $1 increase in sales
Hence, the correct statement is (b)
Read more about average rates at:
https://brainly.com/question/8728504
