what is tan theta when csc theta =2 sqrt 3?
Not really understanding how this works. If possible can someone explain step by step?
Answers
Answer:
[tex]\displaystyle \tan\theta=\frac{\sqrt{11}}{11}[/tex]
Step-by-step explanation:
Trigonometric Identities
If the trigonometric function value of an angle is given, we can find the rest of the trigonometric values of the angle by using one or more of the fundamental identities.
To solve this problem, we need to use the following identities:
[tex]\displaystyle \cot^2\theta=\csc^2\theta-1[/tex]
[tex]\displaystyle \tan\theta=\frac{1}{\cot\theta}[/tex]
Since we are given:
[tex]\displaystyle \csc\theta=2\sqrt{3}[/tex]
And the angle is in the first quadrant, calculate the cotangent:
[tex]\displaystyle \cot^2\theta=(2\sqrt{3})^2-1[/tex]
[tex]\displaystyle \cot^2\theta=4*3-1=11[/tex]
[tex]\displaystyle \cot\theta=\sqrt{11}[/tex]
The tangent is:
[tex]\displaystyle \tan\theta=\frac{1}{\sqrt{11}}[/tex]
Rationalizing the denominator:
[tex]\displaystyle \tan\theta=\frac{1}{\sqrt{11}}*\frac{\sqrt{11}}{\sqrt{11}}[/tex]
[tex]\boxed{\displaystyle \tan\theta=\frac{\sqrt{11}}{11}}[/tex]
Related Questions
Find the relation and solve the answers. Options are given below.
Answers
Answer:
The correct option is;
A. 453
Step-by-step explanation:
The given numbers are not related by factors, because the factors of 779 are 1, 19, 41, and 779
Similarly the factors of 926 are 1, 2, 463, 926
Therefore, the numbers are related by direct association of each digit of the central number to each of the three numbers on the vertices of the triangle as follows;
For the first triangle, we have the numbers at the vertices are; at the top, 14, at the bottom left is 21, and at the bottom right is 36, we have;
Top number divided by 2 gives 14/2 [tex]{}[/tex] = 7
Bottom left number divided by 3 gives 21/3 [tex]{}[/tex] = 7
Bottom right number divided by 4 gives 36/4 = 9
From which we have the number at the center which is 779
Similarly, for the second triangle, we have the numbers at the vertices are; at the top, 18, at the bottom left is 6, and at the bottom right is 24, we have;
Top number divided by 2 gives 18/2 [tex]{}[/tex] = 9
Bottom left number divided by 3 gives 6/3 [tex]{}[/tex] = 2
Bottom right number divided by 4 gives 24/4 = 6
From which we have the number at the center which is 962
Therefore, when we have, the numbers at the vertices as follows;
At the top, 8, at the bottom left is 15, and at the bottom right is 12, we have;
Top number divided by 2 gives 8/2 [tex]{}[/tex] = 4
Bottom left number divided by 3 gives 15/3 [tex]{}[/tex] = 5
Bottom right number divided by 4 gives 12/4 = 3
From which we have the number at the center is 453.
one third of a land is on maize, a fifth of the remainder is on potatoes and the rest which is 0.5 ha is on beans. how much of the land is on potatoes?
Answers
Answer: [tex]1250\ m^2[/tex]
Step-by-step explanation:
Let x= Total land.
Then for Maize = [tex]\dfrac{x}{3}[/tex]
For Potatoes = [tex]\dfrac15(x-\dfrac {x}{3})=\dfrac15(\dfrac{2x}{3})=\dfrac{2}{15}x[/tex]
For beans = [tex]x- (\dfrac{x}{3}+\dfrac{2}{15}x)=0.5 \ ha[/tex]
[tex]\Rightarrow\ x- (\dfrac{5x+2x}{15})=0.5 \ ha\\\\\Rightarrow\ x- (\dfrac{7x}{15})=0.5 \ ha\\\\\Rightarrow\ \dfrac{15x-7x}{15}=0.5 \ ha\\\\\Rightarrow\ \dfrac{8x}{15}=0.5 \ ha\\\\\Rightarrow\ x=0.5\times\dfrac{15}{8} \ ha\\\\\Rightarrow\ x=0.9375 \ ha[/tex]
1 ha = 10000.00 m²
0.9375 ha = 9375 m²
Land for potatoes = [tex]\dfrac{2}{15}(9375) =1250\ m^2[/tex]
Hence, [tex]1250\ m^2[/tex] of the land is on potatoes.
Assuming that any skirt can be paired with any blouse, in how
many ways can Anna select her outfit? List the possibilities.
Answers
andrew needs to call his 8 baseball teammates to make plans for a party at the end of the season if each call takes 5 minutes how much time will he spend making the calls?
A. 1/3 hour
B.40/100 hour
C.2/3 hour
D.3/4 hour
Answers
Answer:
C
Step-by-step explanation:
8*5=40 minutes
There is a total of 60 minutes.
So:
40/60 = 4/6 = 2/3
Change the word sentence into a mathematical equation. Tell what each variable represents.
1. A music club membership costs $17.00 and $7.00 per CD.
2. The total cost of a carpet is $3.00 times the number of square feet.
3. The amount of money you earn for allowance is $20 times the number of months.
4. The cost of belonging to a fitness club is $200 to join and $30 a month in membership dues.
Answers
Answer:
1. $17 + $7C.
This equation provides the total cost if you want to purchase a music CD along with a music club membership. C represents the amount of CDs you wish to purchase, and since each CD costs $7, the amount of money you would need to purchase C amount of CDs is $7C.
2. $3A.
This equation provides the total cost of the area of carpet you want to purchase. A represents the area of the carpet that you want to purchase, measured in square feet as provided by the question, and since each square foot costs $3, the total cost is $3A.
3. $20M.
This equation provides the total money you earn for allowance after M months. M is the number of months that have passed, and since you earn $20 for allowance every month, the total allowance you have earned is $20M.
4. $200 + $30M.
This equation provides the total cost for joining and staying in a fitness club for M months. The initial cost, $200, is applied no matter how many months you join, so we add it from the start; since each month, M, you have to pay $30, the total amount of membership dues is $30M.
Step-by-step explanation:
Hope this helped!
What is sin 28°?
I need help ASAP
Answers
Answer:
sin 28° = 8/17
Step-by-step explanation:
sin A = opp/hyp
sin 28° = 8/17
The value of sin 28° is: sin 28° = 8/17
So, Option B is correct.
Here, given that, a right angle triangle has hypotenuse = 17 units,
height = 8 units,
base = 15 units.
now, we have, the angle between hypotenuse and base is: sin 28°.
from trigonometry we know that,
sin A = opp/hyp
so, here, we get, sin 28° = height/hypotenuse
putting the values, we have,
sin 28° = 8/17
Hence, The value of sin 28° is: sin 28° = 8/17
So, Option B is correct.
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At a six grade graduation celebration there are 80 students and 40 parents.What fraction of the ratio of students to the total number of people at the graduation
Answers
Answer:
2/3
Step-by-step explanation:
Given that:
Number of students = 80
Number of parents = 40
fraction of the ratio of students to the total number of people at the graduation
Total number of people at graduation =. (number of students + number of parents)
80 + 40 = 120
Number of students : total people
80 : 120
80/120 = 8/12 = 2/3
BRO I NEED HELP THIS DUE IN 4 MINS!
Answers
Answer:
440 computers in warehouse B
Step-by-step explanation:
1030=A+B
A=b+150
replace the formula.
a=b+150
so replace the "a"+b=1030
so then it'd be b+150+b=1030
now that's easy.
2b+150=1030
-150 -150
2b=880
/2 /2
b=440
how to solve using Substitution or Elimination??? Help!!!
y=3x-1
y=2x+2
Answers
Y=3x-1
Y=2x+2
2x+2=3x-1
2=x-1
X=3
3(3)-1=y
9-1=y
8=y
Answer:
x=3
y=8
Step-by-step explanation:
the given equations are y=3x-1 --------(1)
and y=2x+2---------(2)
Using substitution method,
and solving y=3x-1
y+1=3x
or y+1/3 =x ------(3)
Putting the value of x= y + 1 / 3 in equation 2
y= 2x+2
or, y = 2 ( y + 1/3) +2
or, y= 2y + 2 / 3 +2
or, y = 2y + 2 + 6 // 3 ( Taking LCM)
Or, 3 y = 2y + 2 + 6 ( the denominator gets multiplied to y)
OR, 3 Y - 2Y =6 PLUS 2
or y = 8
therefore, y=8
now substituting the value of y=8 in equation (3)
y + 1 /3 = x
or ,,, 8 plus 1 by 3 =x
or,,,,, 9 by 3 =x
Therefore, x is 3
NEED HELP ASSP!! please help!!??
Answers
Answer:
Step-by-step explanation:
this is a 30 60 90 triangle.. b/c 2 of the angles are given and you know the total is 180 around a triangle so the last angle is 30
also you know the hypotenuse of this triangle is 10 so use cos and sin to figure out the other sides
Use SOH CAH TOA to remember how the sin and cos functions fit on the triangle
CAH = Cos(Ф) = Adj/ Hyp we are given the Ф angle and we know the hypotenuse so solve for the Adj side
Hyp*Cos(Ф)= Adj
10 * Cos(60) = Adj
5 = Adj = y
Use Sin for the other side and the mnemonic to remember how it fits on the triangle and solve for the Opposite , since we don't know that .. yet
Sin(Ф) = Opp/ Hyp
Hyp * Sin (Ф) = Opp
10 * Sin(60) = Opp
10 *[tex]\sqrt{3}[/tex]/2 = Opp
5*[tex]\sqrt{3}[/tex] = Opp = x
:) I know Sin(60) = [tex]\sqrt{3}[/tex]/2 from a table and also my memory .. know that one from memory
The graph of a linear system is shown.
y
5
7-6-5-4-3-2-1,
2 3 4 5 6 7 8
What is the solution to this linear system? Enter a value in each box to create an ordered pair.
Answers
Answer:
(-1, 7)
Step-by-step explanation:
From the graph attached,
There are two lines representing the system of linear equations.
Solution of two linear equations is represented by a common point or point of intersection on the graph.
Point of intersection of the linear system of equations given in the graph → (-1, 7)
Therefore, solution of the linear system is (-1, 7).
30 points each answer Math
After being rearranged and simplified, which of the following equations could be solved using the quadratic formula? Check all that apply.
Choices are in picture. Please only real answers.
Answers
Answer:
B and D (another answer but not sure about the other one)
Answer: A and B
Step-by-step explanation: I just did it
Help how do I do this?
Answers
Answer:
THE ANSWER IS 9
bc you will distribute 2x+16-2 18÷2 =9
Help me please ASAP!
Answers
Answer:
Choice 1
Choice 4
Choice 5
Step-by-step explanation:
For this one you just have to plug in the x in every equation and solve it. If the answer is true it's true, but if it's false it's false.
Let's solve each of these...
Number 1:
[tex]9-3x=0\\9-3(3)=0\\9-9=0\\0=0[/tex]
As you can see 0 does equal itself so this one is true.
Number 2:
[tex]3x+1=9\\3(3)+1=9\\9+1=9\\10\neq9[/tex]
10 does not equal 9 so this one would be false.
Number 3:
[tex]5x-7=1\\5(3)-7=1\\15-7=1\\8\neq1[/tex]
This one is also false.
Number 4:
[tex]2x+4=10\\2(3)+4=10\\6+4=10\\10=10[/tex]
This one is true.
Number 5:
[tex]\frac{x}{3}+5=6\\\frac{(3)}{3}+5=6\\1+5=6\\6=6[/tex]
This one is true.
Number 6:
[tex]\frac{9}{x}-1=4\\\frac{9}{(3)}-1=4\\3-1=4\\2\neq4[/tex]
This one is false.
Jimmy and Alex each have a CD collection. • The number of CDs in Jimmy's collection can be represented by x. • The number of CDs in Alex's collection is 4 times the number in Walter's collection. • The total number of CDs in both collections is 205. What is x, the number of CDs in Walter's collection?
Answers
Answer:
x = 41
And, the number of CDs in Walter's collection is 41
Step-by-step explanation:
The computation is shown below;
Given that
The number of CDs in Jimmy collection = x
The number of CDs in Alex's collection = 4x
And, The total number of CDs in both collections is 205
So, the equation is
x + 4x = 205
5x = 205
x = 41
The alex collection is
= 4 × 41
= 164
So, the walter collection is
= 164 ÷ 4
= 41
Which is the solution of the quadratic equation (4y - 3)2 = 72?
( O
A y= 3 +677 and y = 3-6v2
€
D y = 3 +672 and y =
-3-6√
4
O y= 92 and y= -312
4
4
O y = 9/7 and y = 32
Answers
Answer: 2 one number 2
Step-by-step explanation:
It's is number 2
The required solution of the quadratic equation (4y - 3)² = 72 is y = 3 ± 6√2/4. Option A is correct.
What is simplification?
Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.
Here,
Given expression, (4y - 3)² = 72
Simplifying the above expression:
(4y - 3)² = 72
4y - 3 = ±√72
4y - 3 = ±6√2
y = 3 ± 6√2/4
Thus, the required solution of the quadratic equation (4y - 3)² = 72 is y = 3 ± 6√2/4. Option A is correct.
Learn more about simplification here:
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I needddd helpppppppp
Answers
Answer:
B the second one -1/3
Step-by-step explanation:
hopefully this helps
The cost of cloth is directly proportional to the length. A 3.2-metre length of cloth costs $38
Work out the cost of a 2.4-metre length of cloth.
Answers
Answer:
[tex]x = \$28.5[/tex]
Step-by-step explanation:
Given
Variation: Direct Proportion
[tex]3.2m = \$38[/tex]
Required
Determine the cost of 2.4m length
Represent the cost of 2.4m length with x
So, we have:
[tex]3.2m = \$38[/tex]
and
[tex]2.4m = x[/tex]
Cross Multiply:
[tex]3.2m * x = \$38 * 2.4m[/tex]
[tex]3.2 * x = \$38 * 2.4[/tex]
Solve for x
[tex]x = \frac{\$38 * 2.4}{3.2}[/tex]
[tex]x = \frac{\$91.2}{3.2}[/tex]
[tex]x = \$28.5[/tex]
Hence, the cost of 2.4m length is $28.5
Tim incorrectly says
that the solution of the system of equations is
x= -9, y= -4.
System of equations:
6x - 2y = -6
11 = y - 5x
a. What is the correct solution?
b. What error might Tim have made?
Answers
Answer:
a)First, solve and regroup
11=y-5x
y=11+5x.
Plug in:
6x-2(5x+11)=-6
6x-10x-22=-6
-4x-22=-6.
-4x=16
x=-4.
Plug it:
y=11+5(-4)
y=11-20
y=-9.
x,y=-4,-9.
b) The error Tim made is that he confused the x and y.
The correct answer is -4,-9.
He said it was -9,-4.
Hope this helps plz hit the crown ;D
The correct solution is -4,-9 time might have changed x coordinate with y-coordinate
What is a linear equation?
A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
6x-2y = -6...1
11= y-5x...2
(a) Rearranging the 2 equation;
11=y-5x
y=11+5x.
substituting in first equation;
6x-2(5x+11)=-6
6x-10x-22=-6
-4x-22=-6.
-4x=16
x=-4.
Now putting the value of x in second equation;
y=11+5(-4)
y=11-20
y=-9.
x,y=-4,-9.
(b) The error Tim made is; he confused the x and y.
The correct answer will be -4,-9.
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Eduardo attends a slime convention in Louisville, Kentucky. He buys a watermelon slime for $9.00 and a waffle slime for $8.50. Louisville’s sales tax is 6%.
What is the sales tax on this purchase?
If necessary, round the amount of tax to the nearest 100th.
A: Not Here
B: $1.10
C: $1.05
D: $10.50
Answers
Answer:
1.05 dollars will be ur answer ;)
Step-by-step explanation:
What is 40% of 500? Please help!!
Answers
Answer:
40/100 times 500=200
Step-by-step explanation:
Lena makes home deliveries of groceries for a supermarket. Her only stops after she leaves the supermarket are at traffic lights and the homes where she makes the deliveries. The graph shows her distance from the store on her first trip of the day.
Give the domain of the function and relate the domain to the relationship described
Answers
made at traffic lights? Answer: 3
Look at the photo pick A B C D either one explanation not needed thank you! <3
Answers
Answer:
B.4
Step-by-step explanation:
It's asking the absolute value even though -6 is used here. So the answer is 4.
PLS HELP
(the second page has the options)
Answers
please help me out! determine the range of the following graph
Answers
Answer:
[-9,-4]
Step-by-step explanation:
The highest and lowest points this graph gets to on the y axis are -4 and -9 respectively.
This means the range is [-9,-4].
Brackets are used since -9 and -4 are seemingly included.
Subtract to find the value of 15(2/3-2/5)
Answers
Answer:
[tex]4[/tex]
Step-by-step explanation:
Simplify the expression
A farmer is selling apples from his orchard. He uses the equation c = 1.6pto calculate the total cost, c, for every pound of apples, p.
a.) How much does a customer pay for 1 pound of apples?
b.) How much would 8.5 pounds of apples cost?
c.) A customer spent $5.20. How many pounds of apples did they purchase?
Answers
Answer:
A) $1.60
B) $13.60
C) 3 1/4 lb
Step-by-step explanation:
What we know:
A farmer uses the equation c = 1.6p to calculate the total cost, c, for p pounds of apples.
A) 1 pound would cost $1.60, as that is the unit rate.
B) 8.5 * 1.6
8.5 + (0.6 * 8.5)
8.5 + 5.1 = $13.60 for 8 1/2 lbs of apples.
C) 5.2/1.6
52/16
13/4 = 3 1/4 lbs of apple for $5.20
5x + 24 + 5(x + 5)
HELP FAST
Answers
5x+24+5(x+5)
Distribute:
=5x+24+(5)(x)+(5)(5)
=5x+24+5x+25
Combine Like Terms:
=5x+24+5x+25
=(5x+5x)+(24+25)
=10x+49
Answer:= 10x+49
solve for x
10x =-49
10/10x -49/10
x= -4.9
Hope this helps
5x + 24 (5x + 25)
(5x + 5x) + (24 + 25)
= 10x + 49
but if you have to solve for x
10x = 49
10/10 = 0
49/10 = 4.9
x = 4.9
What is eight and two ninths subtracted by 2 and seven ninths
Answers
Answer:
5 4/9
Step-by-step explanation:
8 2/9 - 2 7/9
Converting the numbers from mixed Fraction :
(74/9 - 25/9)
L.C.M = 9
(74 - 25) / 9
= 49 / 9
= 5 4/9
Determine what regions make up the given probabilities - shade the Venn Diagram,