Answers
Since both cot(θ) and cos(θ) are positive, it follows that sin(θ) is also positive:
cot(θ) = cos(θ)/sin(θ) > 0 ===> sin(θ) > 0
Recall the Pythagorean identity:
sin²(θ) + cos²(θ) = 1
Multiplying both sides by 1/sin²(θ) yields another form of the identity,
sin²(θ)/sin²(θ) + cos²(θ)/sin²(θ) = 1/sin²(θ)
1 + cot²(θ) = csc²(θ)
so that
csc(θ) = + √(1 + cot²(θ))
csc(θ) = √(1 + (3/2)²)
csc(θ) = √13/2
By definition of cosecant, we have
csc(θ) = 1/sin(θ)
so that
sin(θ) = 2/√13
Then using the Pythagorean identity once more, we have
cos(θ) = + √(1 - sin²(θ))
cos(θ) = √(1 - (2/√13)²)
cos(θ) = 3/√13
so that, by definition of secant,
sec(θ) = 1/cos(θ)
sec(θ) = √13/3
Related Questions
mrs. jenningswants to take her kids on a field trip to the musem. the bus cost a total 100 and the meusem will charge 2 per student. what is the maximum number od students that mrs. jennings cantake to the meusem without exceeding her budget of 150
Answers
On a budget of $150, Mrs. Jennings will only be able to take 25 kids to the museum.
Mrs. Jennings has $150 in total and has to spend it on the bus and getting the kids into the museum.
After she spends on the bus, she will be left with:
= Budget - Cost of bus
= 150 - 100
= $50
She then spends $2 per kid. The total number of kids she can bring into the museum is:
= Amount remaining/ Cost per kid
= 50 / 2
= 25 kids
In conclusion, she can only take 25 kids.
Find out more at https://brainly.com/question/139108.
What is the quotient? −4 1/2÷(−2 2/3)
Answers
which relation is the function?
Answers
Answer:
A is function.
Step-by-step explanation:
what is the inverse of g?
g(x) = 3/x+7
Answers
Given function :-
[tex]\bf \implies g(x) = \dfrac{3}{x}+7[/tex]
To find its reverse , substitute y = g(x) .[tex]\bf \implies y = \dfrac{3}{x}+7[/tex]
Interchange x and y .[tex]\bf \implies x = \dfrac{3}{y}+7[/tex]
Solve for y .[tex]\bf\implies \dfrac{3}{y}= x -7 \\\\\bf\implies y =\dfrac{3}{x-7} [/tex]
Replace y with f-¹(x) .[tex]\implies\boxed{\red{\bf f^{-1}(x) = \dfrac{3}{x-7} }}[/tex]
70 of 38.20 is what
Have to write at least 20 words sooo
Answers
Which type of rock is shown in each of these photographs?
Answers
Answer:
igneous
Step-by-step explanation:
igneous rocks are made out of molten lava or magma
Answer:
sedimentary rock/igneous rock and Metamorphic rock
Step-by-step explanation:
PLEASE HELP ME ITS ALGEBRA THANK YOUUUU
Answers
Answer:
722 kg
Step-by-step explanation:
551:29=x:38
551*38=29x
20938/29=x
x=722 kg
a car travels at an average speed of 64 miles per hour. How long does it take to travel in 3 hours and 30 minute
Answers
Answer:
4 hours and 30 minutes 288/64 = 4,5
Step-by-step explanation:
PLEASE HELP ME ITS ALGEBRA THANK YOUUUU
Answers
Answer:
8 nights
Step-by-step explanation:
First, you have to find out how many centimeters she knits per night and that can be found by dividing 42 by 6
You get 7, and then you find out how many times 7 must be repeated to make 56
Therefore you get 8 nights
Evaluate.
-11.9
-1
Enter your answer in the box.
Answers
-11.9 -1 = -12.9
Your answer is negative 12.9
Answer:
-12.9
Step-by-step explanation:
Hope this helps you! :)
The ages of three brothers are consecutive, even integers. If the sum of the first even integer, three times the second even integer and twice the third even integer is fifty. Find the ages of all three brothers
Answers
Answer:
The ages of all three brothers are 4,6,8 years.
Step-by-step explanation:
Here n is the smallest of the three consecutive even integers, the condition gives you this equation
2n + 3*(n+2) + (n+4) = 34.
2n + 3n + 6 + n + 4 = 34
6n = 24
n = 4.
Answer. The ages are 4, 6 and 8 years.
Hope this helps you.
The ages of the three brothers are 6, 8, and 10 years, respectively.
How to determine ages of the three brothersLet the ages of the three brothers be \(x\), \(x+2\), and \(x+4\).
The sum of the first even integer, three times the second even integer, and twice the third even integer is fifty:
\[x + 3(x+2) + 2(x+4) = 50\]
Simplify the equation:
\[x + 3x + 6 + 2x + 8 = 50\]
Combine like terms:
\[6x + 14 = 50\]
Subtract 14 from both sides:
\[6x = 36\]
Divide by 6:
\[x = 6\]
So, the ages of the three brothers are 6, 8, and 10 years, respectively.
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Use function notation to write the equation of the line. PLEASE ANSWER ASAP
Answers
Answer:
option 2: f(x) = 4x + 4
Step-by-step explanation:
Graph is positive, so with this you should already know that options: 1, 3, 4 are incorrect since those are negative.
However, let's break it down more.
To write the function for a line, you use y = mx+b
m stands for the rise/run
b stands for the y-intercept
Rise over run is 4/1, or just 4
With this we know that option 3 is not correct, yet again
Our y intercept is 4
With this we know that option 1 is not correct, yet again
This just leaves option 2 and 4 with the correct slope and y-intercept, yet as we said before this is a positive slop, so again, 4 is incorrect
Orlando bought a new couch for 1,968, using the furniture store's finance plan. He will pay 164 a month for 12 months. Which equation can Orlando use to find out how much money he still owes after each month of the plan?
a) y = 164x - 1,968
b) y =1,968 - 164x
c) y = 164x
d) y= 1,968 + 164x
Answers
Answer:
B
Step-by-step explanation:
Total(1,968) - x(164) = new value
Let $\overline{AB}$ and $\overline{CD}$ be chords of a circle, that meet at point $Q$ inside the circle. If $AQ = 6,$ $BQ = 12$, and $CD = 38$, then find the minimum length of $CQ$.
Answers
9514 1404 393
Answer:
2
Step-by-step explanation:
The products of chord lengths are the same for the intersecting chords:
AQ×BQ = CQ×DQ
6×12 = CQ×(38 -CQ)
This gives a quadratic in CQ:
CQ² -38CQ +72 = 0 . . . . . write in standard form
(CQ -2)(CQ -36) = 0 . . . . . factor the quadratic
CQ = 2 or 36 . . . . . . . values of CQ that make the factors zero
The minimum length of CQ is 2 units. (DQ will be 36.)
Instructions: Create a table of values for the given function.
Function: f(x) = -4x + 3
Answers
Answer:
Domain: {-2, -1, 0, 1, 2}
Range: {-5, -1, 3, 7, 11}
Step-by-step explanation:
Given the function, f(x) = -4x + 3:
We could simply substitute the given x-values into the function to solve for its corresponding y-values:
x = -2:
f(-2) = -4(-2) + 3
f(-2) = 8 + 3
f(-2) = 11
x = -1:
f(-1) = -4(-1) + 3
f(-1) = 4 + 3
f(-1) = 7
x = 0:
f(0) = -4(0) + 3
f(0) = 0 + 3
f(0) = 3
x = 1:
f( 1 ) = -4( 1 ) + 3
f( 1 ) = -4 + 3
f( 1 ) = -1
x = 2:
f(2) = -4(2) + 3
f(2) = -8 + 3
f(2) = -5
Attached is a screenshot of the table containing the same solution displayed in this post.
How are x and y related in the equation 7 (x - y) = 0?
O = -Y
O x=y
O 7x = y
O 7x = -Y
Answers
Evaluate the expression.
{[(20 – 32) = (-6)}? – 11} = (–7)
What is the value of the expression?
Enter your answer in the box.
Answers
please mark this answer as brainlist
The value of the numerical expression {[(20 – 32) ÷ (–6)]² – 11} ÷ (–7) will be 1.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
The expression is given below.
⇒ {[(20 – 32) ÷ (–6)]² – 11} ÷ (–7)
Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction are all part of the PEMDAS formula. To answer the problem properly and accurately, this rule must be followed.
⇒ {[(20 – 32) ÷ (–6)]² – 11} ÷ (–7)
⇒ {[(–12) ÷ (–6)]² – 11} ÷ (–7)
⇒ {[2]² – 11} ÷ (–7)
⇒ {4 – 11} ÷ (–7)
⇒ (– 7) ÷ (–7)
⇒ 1
The value of the numerical expression {[(20 – 32) ÷ (–6)]² – 11} ÷ (–7) will be 1.
More about the value of the expression link is given below.
https://brainly.com/question/23671908
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(10)/(4)<(z+8)/(2)<(22)/(4)
Answers
Answer:
-3 < z < 3
Step-by-step explanation:
×4
10 < 2z + 16 < 22. -16
-6 < 2z < 6. ÷2
-3 < z < 3
Solve pls brainliest!
Answers
Answer:
18 + v = 67
Step-by-step explanation:
v represents Victor's age, and 18 more than it is 67.
Add 18 to Victor's age, resulting in 67.
The equation is 18 + v = 67.
Which of these is a correct statement about the function graphed below?
5
A. Its equation is y = 2x, so it is not a linear function.
B.
Its equation is y = 2x, so it is a linear function.
c. Its equation is y
2", so it is not a linear function.
D. Its equation is y
2", so it is a linear function
Answers
Answer:
C
Step-by-step explanation:
It curves so it automatically means it isn't any of the answers that say it is.
Numbers with variable powers are NEVER linear, so it is C.
Same question, but different answer option.
I definitely need help with this math problem.
Which expression is equivalent to 10f-5-5f+2?
15f-3 5f-7
15f-7 or -3+6f
Answers
Answer:
5f - 3, I'm assuming there was a typo in the answer choices.
Step-by-step explanation:
10f - 5f + 2 - 5
5f - 3
if Austin burns 120 calories per 30 minutes of weight training how many calories would he burn in 10 minutes?
please help I have a test in 1 hour and I need to know this by then!
Answers
Answer:
40 calories per 10 min
Step-by-step explanation:
Because 30 divided by 3 is 10 and 120 divided by 3 is 40
Graph the lines: y= 4x, y = – 4, and x = - 2.
Answers
I graphed the line, y = 4x, by using the y-intercept (0 ,0), and used the slope (m = 4) to plot other points: {(-1, -4), (1, 4)}.
For y = -4, it is a horizontal line (y = b) with a zero slope. Therefore, regardless of the x-value, its corresponding y-coordinate will be the same (y = -4). To graph the line for y = -4, start at y = -4 and create a horizontal line from there.
For x = -2, it is a vertical line (x = a) with an undefined slope. A vertical line has undefined slope because all points the line have the same x-coordinate. Thus, regardless of the y-value, its corresponding x-coordinate will always be x = -2. To graph the graph, I started at point (-2, 0), and created a vertical line from there.
Please mark my answers as the Brainliest if you find my explanations helpful :)
Given triangle TVU list the sides of the shortest to longest
Answers
Answer:
VU, VT, TU
Step-by-step explanation:
List the side lengths of triangle TUV from shortest to longest.
A. VU, VT, TU
B. VT, TU, VU
C. VT, VU, TU
D. VU, TU, VT"
help it do today help meeee
Answers
The distance from Ellen's home to her school is 4 miles. If she has already traveled 2 miles, how far does she have to go?
Answers
Answer:
6 miles
Step-by-step explanation:
Your itinerary contains a grid map of New York, with each unit on the grid representing 0.25 miles. If the Rockefeller Center is located at (2,−1) and Central Park is located at (7,−6), what is the direct distance (not walking distance, which would have to account for bridges and roadways) between the two landmarks in miles? Round your answer to two decimal places, if necessary.
Answers
Answer:
Its 5
Step-by-step explanation:
5 mhm.
help meeee again ¾÷⅕ =
Answers
Answer:
decimal: 2.25
fraction: 9/4
Step-by-step explanation:
Answer:
Fraction: 15/4
Decimal: 3.75
HELP LAST ATTEMPT !?!!
Answers
Answer:
x=21
Step-by-step explanation:
10+2x+128=180 [Angles in a straight line]
2x=180-138
x=42/2
x=21
Which is the best definition of coefficient?
A letter that represents an unknown value.
O A number that itinultiplied by a variable.
Operations that "undo" each other.
O A fixed value that does not change.
Answers
Answer:
A number multiplied by a variable.
Step-by-step explanation:
For example, 4 is a coefficient.
[tex]4x[/tex]
