Answers
Hi!
Let's first expand the cotangent of theta.
You'll probably know that tangent will be "y/x", or [tex]\frac{sin(x)}{cos(x)}[/tex], and cotangent is the reciprocal of this, meaning that it is "x/y" or [tex]\frac{cos(x)}{sin(x)}[/tex].
That means that we are now given this equation.
[tex]cos(x)\frac{cos(x)}{sin(x)}+sin(x)[/tex]
That'll multiply to:
[tex]\frac{cos^2(x)}{sin(x)}+sin(x)[/tex]
We'll want a common denominator to add by multiplying [tex]sin(x)[/tex] to both top and bottom of the second term:
[tex]\frac{cos^2(x)}{sin(x)}+\frac{sin^2(x)}{sin(x)}[/tex]
[tex]\frac{cos^2(x)+sin^2(x)}{sin(x)}[/tex]
Pythagorean Identity states that [tex]sin^2(x)+cos^2(x)=1[/tex], so substitute that in:
[tex]\frac{1}{sin(x)}[/tex]
Which simplifies to:
[tex]csc(x)[/tex]
Hope this helps!
Related Questions
When the angle of elevation to the sun is 52", a tree casts a shadow that is 13 feet long. What is
the height of the tree? Round to the nearest tenth.
Answers
Answer:
72
Step-by-step explanation:
Answer:
x=10.156713
Step-by-step explanation:
tan(52)=13/x
What is the area of this shape?
A. 42 cm squared
B. 35 cm squared
C. 26 cm squared
D. 14 cm squared
Answers
Answer:
A. 42 cm²
Step-by-step explanation:
Rectangle Area: lw
Put the measurements into the expression
(7)(5)
7•5 = 35
Triangle Area: 1/2bh
1/2(7)(2)
1/2(14)
7
Add them together: 35 + 7 = 42 cm²
30=-6x+6
Solve the equation
Answers
Answer:
-4
Step-by-step explanation:
24 = -6x
-4 = x
............
Answer:
x = -4
Step-by-step explanation:
30 = - 6x + 6
- 6x = 30 - 6
- 6x = 24
- x = 24 / 6
- x = 4
x = - 4
Josie runs a 25-mile race in 5 hours. What is her speed in miles per hour?
Answers
.……………….....
YOOOO SOMEONE HELP ME
Answers
Answer:
180 degrees in either direction
Step-by-step explanation:
picture it on a piece of paper, if you turn it once, the image becomes longer vertically, but if you flip it again, it looks like it does originally. If this is confusing, actually draw it and see how many times you need to rotate the page to make it look identical to the one you posted. 1 turn = 90 degrees.
I need help with this please
Answers
Answer:
polygons
Step-by-step explanation:
this is a hexagon so the sum of interior angles is 720. so add all of those angles and expressions and set it equal to 720. collect like terms and solve for x
once you have x, evaluate and get the exact angle measurements.
Can someone please check if it’s correct??
Answers
Answer:
these both are ture
Step-by-step explanation:
QUICK PLEASE!!!
answer this question and show work or have an explanation.
Answers
Answer:
70
Step-by-step explanation: Triangle angle sum theorem states the interior angles of a triangle sum to 180 degrees. We know one angle is 40 degrees and the two remaining angles are equal in measure.
Since angle J and angle L are equal in measure we can substitute 2x for angles J and L into the equation.
40 + 2x = 180. Subtract 40 from both sides.
2x = 140. Divide both sides by 2.
X = 70
HELPPPPPPP!!!!!! i need this today
Answers
Answer:
(d) 78√3
hope it is right answer for it !!
What is the average rate of change over the interval 1≤x≤3
Answers
9514 1404 393
Answer:
3
Step-by-step explanation:
The average rate of change is the slope of the line between the points at the ends of the interval: (1, -2) and (3, 4). That is given by the slope formula ...
m = (y2 -y1)/(x2 -x1)
m = (4 -(-2))/(3 -1) = 6/2
m = 3
The average rate of change on the interval is 3.
Hello can someone pls help me with this!
Answers
Answer:
slope = 6x
Step-by-step explanation:
the formula to find slope between 2 points is "m = (y2 - y1)/(x2-x1)", or "m = rise/run". so when you plug in the numbers, you get "m = (12 - 6)/(2 - 1)", which gives you "m = 6/1", which is just 6x.
Answer:
Slope = 6
Step-by-step explanation:
From the graph we get:
(x1, y1) = (1, 6) and
(x2, y2) = (2, 12)
Slope = (y2 - y1) / (x2 - x1)
= (12 - 6) / (2 - 1)
= 6 / 1
= 6
What is the quotient of 2.262 and 0.13? Select one: A. 11.5 B. 12.3 C. 15.9 D. 17.4
Answers
Which of the following is an inequality sentence?
[tex] \text{A. \: \: x + 5 = 20}[/tex]
[tex] \text{B. \: \: x = 5}[/tex]
[tex] \text{C. \: \: x < 5}[/tex]
[tex] \text{D. \: \: x + 5}[/tex]
Answers
Answer:
[tex]C. x<5[/tex]
Step-by-step explanation:
Option A [tex][x+5=20][/tex]tells us that: When we add 5 to a variable x, we get 20. As it has a unique value for x and is completely equal to it(i.e. 15), It is an equality.Option B[tex][x=5][/tex] tells us that: A variable x equals to 5. Hence, as x is unique for 5 and is wholly equal to it, it's an equality too.Option C[tex][x<5][/tex] tells us that: A variable x isn't 5 but lesser than it. As we cannot equate it to 5, nor we are given the nature of the variable x, it is an Inequality.Option D[tex][x+5][/tex] is an expression; It can't be called an equation or an inequality unless we relate it with another expression.Step-by-step explanation:
C.x<5 is an inequality sentence.
What story does the graph tell about the turtle's
journey?
Need fast
Answers
matt is standing on top of a cliff 305 feet above a lake. the measurement of the angel of depression to a boat on the lake is 42 degrees. how far is the boat from Matt?
Answers
Answer:
Distance of boat from Matt = 274.5 ft (Approx.)
Step-by-step explanation:
Given:
Height of cliff = 305 ft
Angle = 42°
Find:
Distance of boat from Matt
Computation:
Tan 42° = Distance of boat from Matt / Height of cliff
0.90 = Distance of boat from Matt / 305
Distance of boat from Matt = 274.5 ft (Approx.)
Mr. Burns organized the grades for 11 students in the boxplot below. None of the students earned the same grade. What percent of grades are between 79 and 84?
A. 100%
B. 25%
C. 50%
D. 75%
Answers
Answer:
C
Step-by-step explanation:
Answer: 25%
Step-by-step explanation: Sorry this is late
х
4.8 ft
6.5 ft
3.8 ft
The illustration models a shadow cast by a palm tree and the shadow of an individual at 5 o'clock each day. To the nearest tenth,
how tall is the palm tree?
Answers
Answer:
8.2FT
Step-by-step explanation:
Answer:
The answers 8.2!!
Step-by-step explanation:
I just guessed on the usatestprep and got it lol
The main height of a basketball team is 6 feet with the standard deviation of 0.2 feet. The team center is 6.9 feet tall. Find the center Z score. Is the score unusual?
Answers
Complete Question
The mean height of a basketball team is 6 feet with the standard deviation of 0.2 feet. The team center is 6.9 feet tall. Find the center Z score. Is the score unusual?
Answer:
Center Z score = 4.5
The score is unusual
Step-by-step explanation:
The mean height of a basketball team is 6 feet with the standard deviation of 0.2 feet. The team center is 6.9 feet tall. Find the center Z score. Is the score unusual?
The formula for z score is:
z = (x-μ)/σ, where
x is the raw score = 6.9feet
μ is the population mean = 6feet
σ is the population standard deviation = 0.2 feet
Hence:
Z = 6.9 - 6/0.2
Z = 0.9/0.2
Z = 4.5
Yes this score is unusual
Two different counting numbers from 1 to 10 were randomly chosen. What is the probability that the larger one is a multiple of the smaller one?
Answers
Answer:
7/10
Step-by-step explana
7/10 was the answer
Answer:
7/10
Step-by-step explanation:
Which function is equivalent to y=3(x−2)^2+6?
y=3x^2−12x+30
y=3x^2+10
y=3x^2−4x+10
y=3x^2−12x+18
Answers
2. A mother is three times as old as her daughter.
In 12 years' time she will be twice as old as her daughter will be then.
How old is the mother no.w?
Answers
At the beginning the mother is 36 and the daughter is 12. Making her 3 times older. In 12 years the daughter would be 24 and the mother would be 48. Making her twice as old as her daughter
Answer:
The mother is 36 years now.Step-by-step explanation:
x - the age of the daugther now
3x - the age of the mother now
x + 12 - the age of the daugther in 12 years' time
3x + 12 - the age of the mother in 12 years' time
The mother will be twice as old as her daughter will be then:
3x + 12 = 2·(x + 12)
3x + 12 = 2x + 24 {subtract 2x from both sides}
x + 12 = 24 {subtract 12 from both sides}
x = 12 (the age of the daughter now)
3x = 3·12 = 36
PLS HELP!!!!
Why are the x-values nonnegative ?
Answers
Answer:
Because the slope is going up and not down?
Step-by-step explanation:
Answer:
because the y -values is nonnegative so the x-values are the opposite of the y-values
16x2-1
O A. (2x - 1)(8x - 1)
O B. (4x - 1)(4x + 1)
O C. (2x - 1)(8x + 1)
O D. (4x - 1)(4x - 1)
Help
Answers
Answer:
D is the answer (4x - 1)(4x + 1)
Please mark as brainliest
Have a great day, be safe and healthy
Thank u
XD
If the midpoint of the line segment is AB has coordinates (3, -1) and A (-5,0) then:
B=
Answers
Tom's earnings vary directly with the number of hours he works. Suppose that he worked 9 hours yesterday and earned $126. How much will he earn today if he works 8 hours?
Answers
hope this helped :)
the number of subscribers f(t) to a newspaper after t years is shown by the equation below f(t) = 75(.95)^t
Answers
The above equation can be rewrite as
which is equivalent to the exponential decay function with rate r=0.05=5%
⇒ The number of subscribers to a newspaper decreased by 5% every year.
1x+2x+3x=180 find the measure of each angles.
Answers
Answer:
x=30 is the answer no hate if I'm wrong :)
Step-by-step explanation:
The sum of angles in a triangle is 180 so we add them all and we get x=30.
Then find the measure of each angle by substitution.
Which of the following systems of linear equations has no solution?
Answers
Answer:
3rd choice
Step-by-step explanation:
The answer is the 3rd choice.
x cannot be 3 and 5 at the same time.
x = 3
x = 5
Subtract the first equation from the second equation.
x - x = 5 - 3
0 = 2
Since 0 = 2 is a false statement, there is no solution.
Answer: 3rd choice
Classify the triangle described below.
A triangle with measures of x∘, x∘, and 2x∘ is a(n)
triangle.
A triangle with measures of x∘, x∘, and 2x∘ is a(n)
blank triangle.
Answers
9514 1404 393
Answer:
isosceles right
Step-by-step explanation:
The three angles total 180°, so you have ...
x° +x° +2x° = 180°
4x = 180
x = 45
2x = 90
The largest angle is a right angle (90°).
A triangle with measures of 45°, 45°, and 90° is an isosceles right triangle.
In a game, the player wins if he rolls a 4 on a number cube (six sides). If the number cube is rolled 24 times, then what is a reasonable prediction for the number of times a 4 will be rolled?
Answers
Answer:
6
Step-by-step explanation:
ℎ 4 6
[tex]24 \div 4 = 6[/tex]