Answers
Answer: Choice A
[tex]\tan(\alpha)*\cot^2(\alpha)\\\\[/tex]
============================================================
Explanation:
Recall that [tex]\tan(x) = \frac{\sin(x)}{\cos(x)}[/tex] and [tex]\cot(x) = \frac{\cos(x)}{\sin(x)}[/tex]. The connection between tangent and cotangent is simply involving the reciprocal
From this, we can say,
[tex]\tan(\alpha)*\cot^2(\alpha)\\\\\\\frac{\sin(\alpha)}{\cos(\alpha)}*\left(\frac{\cos(\alpha)}{\sin(\alpha)}\right)^2\\\\\\\frac{\sin(\alpha)}{\cos(\alpha)}*\frac{\cos^2(\alpha)}{\sin^2(\alpha)}\\\\\\\frac{\sin(\alpha)*\cos^2(\alpha)}{\cos(\alpha)*\sin^2(\alpha)}\\\\\\\frac{\cos^2(\alpha)}{\cos(\alpha)*\sin(\alpha)}\\\\\\\frac{\cos(\alpha)}{\sin(\alpha)}\\\\[/tex]
In the second to last step, a pair of sine terms cancel. In the last step, a pair of cosine terms cancel.
All of this shows why [tex]\tan(\alpha)*\cot^2(\alpha)\\\\[/tex] is identical to [tex]\frac{\cos(\alpha)}{\sin(\alpha)}\\\\[/tex]
Therefore, [tex]\tan(\alpha)*\cot^2(\alpha)=\frac{\cos(\alpha)}{\sin(\alpha)}\\\\[/tex] is an identity. In mathematics, an identity is when both sides are the same thing for any allowed input in the domain.
You can visually confirm that [tex]\tan(\alpha)*\cot^2(\alpha)\\\\[/tex] is the same as [tex]\frac{\cos(\alpha)}{\sin(\alpha)}\\\\[/tex] by graphing each function (use x instead of alpha). You should note that both curves use the exact same set of points to form them. In other words, one curve is perfectly on top of the other. I recommend making the curves different colors so you can distinguish them a bit better.
Related Questions
The circumference of a circle is 6pi inches. What is the area of the circle
Answers
Answer:
B0 A = 9 Pi
Step-by-step explanation:
c = 6 Pi (given)
c = Pi 2r (standard formula)
r = c / (2 Pi)
r = 6 Pi / (2 Pi) = 3 (substitute 6 Pi for c)
So
A = Pi r**2
A = Pi 3**2
A = 9 Pi
An airplane travels 4374 kilometers against the wind in 6 hours and 5514 kilometers with the wind in the same amount of time. What is the rate of the plane in
still air and what is the rate of the wind?
Answers
Answer:
air = 95 mph
plane = 824 MPH
Step-by-step explanation:
6(x-y) = 4374
6(x+y)= 5514
6x - 6y = 4375
6x + 6y = 5514
12x = 9889
x = 824 mph
y = 95 mph
If a point is equidistant from the endpoint of segment, then it is
Answers
Hi
.... then it is located on the perpendicular bisector.
Multiple choice: what is the answer?
Answers
Answer:
200kg wt is your answer I think.
9514 1404 393
Answer:
A. 10√7 kg wt
Step-by-step explanation:
The magnitude will be that of the long diagonal of a parallelogram that has sides 10 and 20. It must be more than 20, and cannot be 30 or more. That only leaves one answer choice:
10√7 kg wt
Write 0.0406 in scientific notation.
Answers
Answer:
4.06×10^-2
hope that helps uh..☺
Answer:
Ans; 0.0406 = 4.06 ×10–²
Answer ASAP please!
Answers
Answer:
B
SOH-CAH-TOA
Sin= opp/hyp
Step-by-step explanation:
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Larry is going on a road trip for work. He is recording how many miles he drives, and how many gallons of gas he uses for his expense report. Which is the independent variable?
A. the amount of miles Larry drives
B. the type of roads Larry drives on
C. the type of car Larry drives
D. the amount of gasoline Larry uses
Answers
An independent variable is one that isn't changed by the other variables you are trying to measure.
The amount of miles Larry drives doesn’t depend on anything in this situation.
The question only mentions gallons of gas and miles so I would think you disregard the type of roads Larry drives on and type of car Larry drives.
The amount of gasoline Larry uses is a dependent variable because it depends on the amount of miles Larry drives.
Hope this helps
Write parametric equations of the line [tex]-4x+y=-2[/tex]
a. [tex]x=t, y=4t-2[/tex]
b. [tex]x=t, y=-4t-2[/tex]
c. [tex]x=t, y=4t+2[/tex]
d. [tex]x=t, y=-4t+2[/tex]
Answers
Answer:
Option a
Step-by-step explanation:
Assign a value to variable x =t
Eq becomes
-4t+y=-2
y=4t-2
K is between Jand M. Lis
between K and M. Mis
between Kand N. If JN = 30,
KM = 8, and JK = KL = LM,
what is MJ?
Answers
Answer:
18
Step-by-step explanation:
K is between Jand M. Lis
between K and M. Mis
between Kand N. If JN = 30,
KM = 8, and JK = KL = LM,
what is MJ? Mj is 18
answer for brainlyyyyyy
PLSSS
Answers
[tex]\huge\mathsf\green{ANSWER}:—[/tex]
[tex]option \: \: c \: \: \: \frac{3}{4} \: is \: the \: correct \: option[/tex]
Know more :-Rational numbers are numbers which can be represent in the form of p/q where p and q are integers and q≠0 that's why 3/4 is the correct option
plz mark me as brainliest answerThe second one write it on the paper and take a picture
Answers
Answer:
The common for the second question is 30
Answer:
39/30 Here 30 will be common in denominators
Step-by-step explanation:
6/15×2/2=12/30
3/10×3/3=9/30
3/5×6/6=18/30
= 12/30+9/30+18/30
39/30
Draw a number line that represents 7+(-4).
Answers
Gem and her three friends are going on a holiday.
There is a buy 2 get one free offer on plane tickets.
Tickets cost £400 each.
If Gem and her friends are each expected to pay an equal amount towards their tickets, how much does each person pay?
Answers
Answer:
£200
Step-by-step explanation:
4 friends - 4 tickets
They need to BUY 3 tickets.
3 tickets will cost £1200
Divide the £1200 between the 4 friends which is £300.
They will then get the other 1 ticket for free and have 4 altogether!
the cost of plastering a wall of a room having length 8m and heights 4m at Rs 15 per m² is Rs 1560 . find the cost of carpeting the room at rs 300 per m²
Answers
Step-by-step explanation:
here ,
length = 8m
height=4m
Rate of plastering 4 walls = 15/m^2
Cost of plastering 4 wall = Rs 1560
Area of floor = Cost of plastering / Rate of plastering
= 1560/15
= 104
again,
Area of four wall = 2h(l+b)
or, 104= 2×4(8+b)
or, 104 =8(8+b)
or, 104/8=8+ b
or,13 - 8= b
or, b= 5
again,
Area of floor= l×b
= 8×5
= 40
again,
Rate of carpeting the floor= 300/ m^2
Area of floor = 40 m^2
cost of carpeting=Rate × Area
= 300×40
= 12000
Find the area of the shape. Kahn Academy
Oh
Answers
Answer:
84.78 units²
Step-by-step explanation:
First we must calculate the total area of the circle :
A = pi.r²
= 3.14×36
So total area = 113.04 units²
Then we must divide this area by 4 and subtract it form the total area
113.04÷4 =28.26
The area of the shape = 113.04-28.26
= 84.78 units²
Help with this? Anyone know how to do it? It’s due in the morning
Answers
Using pythagorean theorem
[tex]\\ \sf\longmapsto B^2=H^2-P^2[/tex]
[tex]\\ \sf\longmapsto x^2=13^2-5^2[/tex]
[tex]\\ \sf\longmapsto x^2=169-25[/tex]
[tex]\\ \sf\longmapsto x^2=144[/tex]
[tex]\\ \sf\longmapsto x=\sqrt{144}[/tex]
[tex]\\ \sf\longmapsto x=12[/tex]
Answer:
x = 12
Step-by-step explanation:
→ State Pythagoras theorem
a² + b² = c²
→ Rearrange to make b the subject
b² = c² - a²
→ Square root everything
b = √c² - a²
→ Substitute in the numbers
b = √13² - 5²
→ Simplify
b = 12
You roll a six-sided number cube and flip a coin. What is the probability of rolling a number greater than 1 and flipping heads? Write your answer as a fraction in simplest form.
Answers
Answer:
5/12Step-by-step explanation:
Number cube:
Numbers greater than 1 → 5 options out of 6Coin:
Heads → 1 out of 2Required probability:
P(>1 & H) = 5/6*1/2 = 5/12Answer: Probability of rolling a number more than one: 5/6
Probability of heads: 1/2
Probability of both: 1/2 + 5/6 = 4/3
Step-by-step explanation:
What is the base area of the cone?
Answers
Answer:
Step-by-step explanation:
In order to find the area of the circle base, we need the radius, and we don't have it. We'll use the volume to find the radius, as follows:
[tex]V=\frac{1}{3}\pi r^2h[/tex] and fill in the givens:
[tex]75=\frac{1}{3}\pi r^2(5)[/tex] and solve that for r;
[tex]r=\sqrt{\frac{3(75)}{5\pi} }[/tex] so
r = 3.784698783 and plug that in for the radius to find the area of the circle base:
[tex]A=\pi r^2[/tex] so
[tex]A=\pi (3.784698783)^2[/tex] gives you that
A = 45 meters squared, exactly. No decimal.
What type of triangle has side lengths 2, squareroot12, and 19?
A. acute
B. not a triangle
C. obtuse
D. right
Answers
Answer:
Step-by-step explanation:
Im gonna guess C, not sure. good luck tho
The number of dogs a family has and the amount of floor cleaner used are known to have a strong positive association. Jaylen concluded that the number of dogs causes an increase in floor cleaner usage. Is Jaylen's conclusion valid? Explain.
Answers
Answer:
Jaylen's conclusion is not valid because association does not imply causation.
Step-by-step explanation:
[tex]6 \sqrt{2} - 4 \sqrt{3} + |3 \sqrt{8} - 8 \sqrt{3} | + 2 \sqrt{12} [/tex]Solve this pls ......
Answers
Answer:
8√3 ≈ 13.86
Step-by-step explanation:
6√2 - 4√3 + | 3√(2²•2) -8√3 | + 2√2²•3
Every 2² get our from the square root and loses the ² :
6√2 -4√3 + | 2•3√2 -8√3 | + 2•2√3
Solve the multiplications and taking of the | | , the signal inside it changes:
6√2 - 4√3 +8√3 -6√2 +4√3
Now you group the similar terms and solve the possible operations:
6√2 - 6√2 +4√3 - 4√3 + 8√3
8√3 ≈ 13.86
Step-by-step explanation:
4(3_/2-2_/3)
SEE the IMAGE for Solution
what is the area of the composite shape?
Answers
Answer:
the ...ha answer is =99 in.^3
On a piece of paper graph
f(x) = {-1 if -1 <= x < 0}
{ -2 if 0 <= x < 0}
{ -3 if 1 <= x < 2
Answers
In this question, a piece-wise function is asked to be graphed.
Piece-wise function:
A piece-wise function is a function that has different definitions, depending on the input.
In this question, the function has three different definitions:
For x between -1(inclusive) and 0, y takes a constant value of -1.
For x between 0(inclusive) and 1, y takes a constant value of -2.
For x between 1(inclusive) and 2, y takes a constant value of -3.
Additionally:
At the inclusive points, the interval is circled, and thus, the graphic is given at the end of this answer.
For another example of the graphic of a piece-wise function, you can check https://brainly.com/question/16855064
Answer:
Step-by-step explanation:
1. (1, 3); (2, 3)
2. (0, 0) (1, 0)
3. (-1, 1) (0,0)
What is the only temperature that is the same in Fahrenheit and Celsius?
Answers
Answer: -40 °C and -40 °F.
Step-by-step explanation:
Answer:
-40
Step-by-step explanation:
Let the temperature be x which is the same in Fahrenheit and Celsius. Then it must satisfy the Fahrenheit and Celsius conversion formula which is (Fahrenheit-32)*(5/9)=Celsius
x=(x-32)*(5/9)
9x=5x-160, x=-40
Find the value of x to the nearest tenth.
Answers
Answer:
around 4.1
Step-by-step explanation:
Using Pythaogrean theorem we get sqrt 32 or 4sqrt2 for the diagonal of the square.
To get x we can use Pythagorean theorem again to set up an equation,
32 + x^2 = 49
This gives us x = sqrt17, which is approximately 4.1231 or around 4.1
Answer:
Step-by-step explanation:
8. Which expression is greatest? Justify your answer.
a. 4 X -5
b. -5 + 4
c. -4- (-5)
Answers
Answer:
c
Step-by-step explanation:
i think this is the greatest because if you solve all of the expressions you will find out that this is the greatest.
a.4×-5=-20
b.-5+4=-1
c.-4-(-5)=1
therefore 1 is the greatest so the expression c is the greatest.
I hope this helps
x-1/(x+1)(x-5)
In 10 words or fewer, tell what value of x will make the above rational
expression equal to zero.
Answers
Answer:
x=1
Step-by-step explanation:
x-1/(x+1)(x-5)
When the numerator is equal to zero and the denominator is not equal to zero
x-1= 0
x=1
Write in detail 5 goods that you get using money currency and 5 services that you can get using money currency.
Answers
The goods that money can buy include soap, bag, shoe, radio, television etc. The services that can be gotten include barbing, teaching, tailoring, catering, auditing etc.
Money is important in our everyday lives. We use money to make purchases of goods and it serves as a medium of exchange.
We can use money to buy goods like shoes, jewelry, radio, phone, bag, etc. When we need services such as barbing of our hair, teaching, tailoring, catering, auditing etc, we can make the purchase through money and the services will be given to us.
Read related link on:
https://brainly.com/question/11681948
giải pt sin(x^2-4x)=0
Answers
Answer:
x=0,2half1?(I'm
not sure)
In Game 1, Emerson struck out 30 times in 90 times at bat. In Game 2, he struck out 40 times in 120 times at bat. In Game 3, Emerson struck out 42 times in 140 times at bat. What percentage of times at bat did Emerson actually hit the ball?
Answers
Answer:
Total number of strikeouts:
30 + 40 + 42 = 112Total number of at bats:
90 + 120 + 140 = 350Hits = times - strikeouts:
350 - 112 = 238Percentage:
238/352*100% = 67.61%
