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
Mr. Morgan invested $20,000 in an account earning 4.5% annual interest. How many years would it take for him to earn 5400 in a simple interest
Answers
£20,000 x 0.045 = £900
£5,400 / £900 = 6 years
Pleaseeee help :) and don’t answer unless you really know the answer please
Answers
Answer:
b) simplify the constant
c)isolate the variable by dividing the coefficient
Step-by-step explanation:
Jayden drives 22.5 miles in 30 minutes. If he drove one hour in total at the same rate, how far did he go? Before you try that problem, answer the question below. How many minutes did Jayden drive in total?
Answers
Answer:
Step-by-step explanation:
2
pls help 10 minutes left to submit everything is on the image below
Answers
Answer:
a. 5
b. 1
c. 132
d. -2
Step-by-step explanation:
a. The square root of 4 is 2, the absolute value of -3 is 3. 2 + 3 = 5
b. 4 - (-3) / -7 = 7/ -7 = 1
c. 2 * 4^3 = 128 + (-3) - (-7) = 132
d. 2 (-7 + 3) = -8, square root to the third power of -8 is -2
I hope this helped, please mark Brainliest, thank you!!
Help me please!!!!
Adrienne and Suki simplified the expression -(8) - (-6). Their work is shown
below. *
Adrienne's Work
Suki's Work
-8-(-6)= -14
-8-(-6)=-2
A. Whose answer is correct?
B. Explain the error the other person made.
Your answer
Answers
Answer:
im pretty sure it would be -8-(-6)=-2 for the first one
A container of water holds 128 fluid ounces. Toya drinks 8 fluid ounces of water every hour. How many fluid ounces are in the container after 8 hours
Answers
Answer: 64 fluid ounces
Step-by-step explanation:
Amount of water in the container = 128 fluid ounces
Amount drank by Toya every hour = 8 fluid ounces
For 8 hours, Toya would have drank:
= 8 × 8 fluid ounces
= 64 fluid ounces
To calculate the amount of fluid ounces
thataree in the container after 8 hours, we then subtract 64 fluid ounces from 128 fluid ounces. This will be:
= 128 fluid ounces - 64 fluid ounces
= 64 fluid ounces
Evaluate the algebraic expression for v= 1 and r = 7
6r - |-8+v|
Answers
Answer:
41
Step-by-step explanation:
The absolute value function always gives a positive result, that is
| - a | = | a | = a
Given
6r - | - 8 + v | ← substitute v = 1 and r = 7 into the expression
= 6(7) - | - 8 + 1 |
= 42 - | - 1 |
= 42 - 1
= 41
If DE=2x-1, what is the value of x
1. 7
2. 7.5
3. 8
4. 8.5
Answers
16 = 2x - 1
Add 1 on both sides
17 = 2x
Divide by 2 on both sides
8.5 = x
I believe this is your answer
The value of the variable 'x' will be 8.5. Then the correct option is D.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
In the diagram below, ΔABC with sides of 13, 15, and 16, is mapped onto ΔDEF after a clockwise rotation of 90°.
The side AB is equal to DE. Then we have
DE = AB
2x - 1 = 16
2x = 16 + 1
2x = 17
x = 17/2
x = 8.5
The value of the variable 'x' will be 8.5. Then the correct option is D.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ2
PLEASE HELPPPP 15 POINTS! A man's shoe size is approximately three times his foot length in inches, minus twenty-two. What would be the equation that could represent his shoe size, y, in terms of inches, x?
A. y=3x-22
B. y=22x-3
C. x=3y-22
D. 3x+22
Answers
Answer:
I am sorry
Step-by-step explanation:
I am new
Answer:
a
Step-by-step explanation:
im 100% sure
To factor 9x^2- 4, you can first rewrite the expression as:
O A. (3x-2)^2
O B. (x)^2-(2)^2
C. (3x)^2-(2)^2
D. None of the above
Answers
Answer:
D
[tex](3x - 2)(3x + 2) \\ [/tex]
Will give brainliest if correct.
Answers
Answer:
x-int: (3, 0)
y-int: (0, -3)
General Formulas and Concepts:
Alg 1
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptThe y-intercept is the y value when x = 0.
Another way to reword that is when the graph crosses the y-axis.
The x-intercept is the x value when y = 0.
Another way to reword that is when the graph crosses the x-axis.
Step-by-step explanation:
Step 1: Define equation
x - y = 3
Step 2: Convert to slope-intercept form
Subtract x on both sides: -y = 3 - xDivide both sides by -1: y = x - 3Step 3: Find x/y-intercepts
x-int
Set y = 0: 0 = x - 3Add 3 to both sides: 3 = xRewrite: x = 3Write coordinates: (3, 0)y-int
Set x = 0: y = 0 - 3Subtract: y = -3Write coordinates: (0, -3)Answer:
x=3
y=-3
Step-by-step explanation:
Help plz:))) I’ll mark u brainliest
ASAP!!!
Answers
can someone pls help Write the following equation as a sentence: w = (15)(165)
Answers
Answer:
width equals fifteen times one hundred sixty five
is that right or is that ok or good enough?? sorry if i am wrong....
Answer:
W = 2475
Step-by-step explanation:
I am not sure if you want the answer or not but I hope this helps
Find the equation of a line that passes through the points (6,7) and (8,3).
Leave your answer in the form
y = mx + c
Answers
Answer:
y=-2x+19
Step-by-step explanation:
For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form: m= [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].
Now we have,
m= 3-7/8-6
m=-2. Since m=-2, the equation is y=-2x+b.
To find b, think about what your (x,y) points mean:
(6,7). When x of the line is 6, y of the line must be 7.
(8,3). When x of the line is 8, y of the line must be 3.
Substitute them to the equation y=-2x+b.
You can use either (x,y) point you want..the answer will be the same:
(6,7). y=mx+b or 7=-2 × 6+b, or solving for b: b=7-(-2)(6). b=19.
(8,3). y=mx+b or 3=-2 × 8+b, or solving for b: b=3-(-2)(8). b=19.
So, the equation of the line that passes through the points
(6,7) and (8,3) is y=-2x+19.
6,857 my lessons my stuf The Pythagorean Theorem What is the distance between the points (22,21) and (26,24)?
Answers
Answer:
the distant between 20,21 is 1. and the distant between 26,24 is 2.
Step-by-step explanation:
1. 21-20=1
2. 26-24=2
hope this helps
what is the difference between mutiplying and adding polynomials
Answers
Answer:
When you add polynomials, you combine only like terms together. When you multiply polynomials, you multiply all pairs of terms together.
Step-by-step explanation:
.
Answer:
adding, subtracting and multiplying polynomials are, basically, the same as adding, subtracting and multiplying numbers. They only difference is that we have a pesky variable to worry about
Jimmy and Lauren are
organizing transportation for
a field trip from ACIT. Jimmy
found out that his group has
841 students, and he needs 9
vans and 16 buses to
accommodate. While Lauren’s
group has 351 students, and
she needs 8 vans and 5 buses
for them. How many students
fit in a van and a bus for this
field trip? (please include steps)
Answers
Step-by-step explanation:
Jimmy's group : has 841 students
Lauren's group: has 351 students
9 vans 16 buses
8 vans 5 buses
Vans: V
Buses: B
9v + 16b = 841
9v + 16b = 841
-16b -16b
9v/ 9 = 841 /9 - 16b/9
8( 841/9 - 16b/9) +5b = 351
v - (841/ 9 - 16b / 9 )
8 (841 / 9 - 16b/9) +5b = 351
6728/9 - 128b / 9 +5b = 351
-128b/9 + 45b/9 = -83/9b
6728/9 -83/9
- 6728/9 +83/9 = 3159/9 - 6728/9
(9)83b / 9 = -3569 (9)/9
-83b = -3564
-83 -83
B = 43 students
8v + 5b = 351
8v + 5 (43) = 351
8v + 215 = 315
-215 -215
8v = 136
8 8
V = 17 students
43 students can fit on a bus and 17 students can fit in a van.
- 5.2-(-3.1) + 5.2
I
Answers
Answer:
7.3 I think
Step-by-step explanation:
how to convert root into decimal
Answers
Elijah needs to lease out a music studio to record his new album the studio charges and initial studio-use fee plus an hourly fee for each hours in the studio let P represent the total amount of money Elijah would have to pay to use the studio four t hours A graph of P is shown below write an equation for P then state the Y intercept of the graph and determine its interpretation in the context of the problem
Answers
Answer:
100+50t
Step-by-step explanation:
Answer:
P = 100+50t
The y-intercept of the function is 100 which represents the initial fee of using the studio.
Fond the product of 2x4(2x+3x+4)
Answers
Answer:
10x⁵ + 8x⁴
Step-by-step explanation:
What is the slope-intercept form equation of the line that passes through (2, 4) and (4, 10)? (5 points) a y = −3x − 2 b y = −3x + 2 c y = 3x + 2 d y = 3x − 2
Answers
Answer:
d
Step-by-step explanation:
someone please help !!!
Answers
Explanation: I multiplied
7/3*+1/3=4+5/3x this is a test pls helppp
Answers
Answer:
I am sorry. To answer a test is against the Honor Code, I cannot help you.
Step-by-step explanation:
Remember PEMDAS :)
Answer:
2.125
Step-by-step explanation:
3. Choose the correct statement below:
a) All natural numbers are whole numbers.
b) All whole numbers are natural numbers.
Answers
slope= 1/4, y intercept=2
Answers
Based on the results of the simulation, if Sally's name is represented by diamonds, what is the probability that Sally will win
the free homework pass?
A.52%
B. 24%
C. 8%
D.16%
Answers
Answer:
Step-by-step explanation:
If she's represented by diamonds, then that's 2/25 which is 8%, C
Answer:
Step-by-step explanation:
8%
which ordered pair is a solution of the equation: 2y=7x-3
only 2,4
only 3,9
both 2,4 and 3,9
neither
Answers
Answer:
It is only 3,9.
Step-by-step explanation:
You need to substitute each pair into the equation to find if both side have the same answer, 3,9 is the correct answer because both sides are equal:
2(9) = 7(3)-3
18= 18
The answer is (3,9).
I hope this helps!
Pls help me I have no idea
Answers
Answer:
130 degrees
Step-by-step explanation:
ABF and BFE are alternate angles. So BFE is 65
BG=FG so FBG is 65. x the exterior angle is 65+65=130 degrees
A line has a slope of 2 and passes through the point (0,0) what is its equation in slope intercept form
Answers
Answer:
y=mx+b is slope-intercept form
where m is the slop, and b is the y intercept
if m is the slop then we can plug that into the equation
y=2x+b
next plug in the y intercept which is 0. the y intercept is the y ok the given point. in the point the y is zero making your intercept 0.
y=2x+0
eliminate the 0
y=2x is your equation
Step-by-step explanation: