What is the value of cos(x/2) if tan x=1/2 and x is in quadrant III

Answers

Answer 1

Answer:

Step-by-step explanation:

What Is The Value Of Cos(x/2) If Tan X=1/2 And X Is In Quadrant III
Answer 2

The value of cos(x/2) is required.

The required value is [tex]\cos(x/2)=-\sqrt{\dfrac{5-2\sqrt{5}}{10}}[/tex]

Trigonometry

The 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

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:

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 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

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!

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

slope= 1/4, y intercept=2

Answers

Answer:y = mx + b formaty = 1/4x + 2Hope this helps!!

If DE=2x-1, what is the value of x

1. 7
2. 7.5
3. 8
4. 8.5

Answers

Taking into account the 90° rotation: A is D, B is E, and C is F. So, the corresponding side on Triangle ABC to the side DE(2x - 1) is AB (16).

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

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]

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

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:

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%

Help plz:))) I’ll mark u brainliest
ASAP!!!

Answers

A is 35 degrees...........

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

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

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

- 5.2-(-3.1) + 5.2
I

Answers

Answer:

7.3 I think

Step-by-step explanation:

Your answer is 3.1 because the 5.2’s cancel out since one is negative and the other is positive and you have -(-3.1) left over. Two negatives turn into a positive so -(-3.1)= 3.1

3. Choose the correct statement below:
a) All natural numbers are whole numbers.
b) All whole numbers are natural numbers.

Answers

All natural numbers are whole numbers

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

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!!

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-intercept

The 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 - 3

Step 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:

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:

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

6 years
£20,000 x 0.045 = £900
£5,400 / £900 = 6 years

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:

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

someone please help !!!

Answers

Answer: it A (-36/w^7
Explanation: I multiplied

how to convert root into decimal

Answers

how’d u get 150? because it looks incorrect

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.

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.

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

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