Answers
Recall that sine is the ratio of opposite over hypotenuse, so we say
sin(theta) = opposite/hypotenuse
If we have a triangle labeled as such in the diagram below, then we can use symbols to write sin(theta) = A/C
Similarly, cos(theta) = B/C since cosine is the ratio of adjacent over hypotenuse.
Then from here we use a bit of algebra to compute the left hand side of the given equation. The goal is to see if we can simplify it to 1.
[tex]\sin^2\left(\theta\right)+\cos^2\left(\theta\right)\\\\\left(\sin\left(\theta\right)\right)^2+\left(\cos\left(\theta\right)\right)^2\\\\\left(\frac{A}{C}\right)^2+\left(\frac{B}{C}\right)^2\\\\\frac{A^2}{C^2}+\frac{B^2}{C^2}\\\\\frac{A^2+B^2}{C^2}\\\\\frac{C^2}{C^2}\\\\1[/tex]
So this shows that the left hand side is identically the same as the right hand side (both sides are 1), and it doesn't matter what you replace theta with. Theta can be any real number and the equation will always be true.
Note: if you're wondering how A^2+B^2 became C^2, it's because of the pythagorean theorem. So that's why this trig identity is often referred to as the pythagorean trig identity.
Related Questions
If p(x) = x^3 + 3x^2 - 2x + 4, then find the value of
p(2) + P(-2) - (0)
Answers
Answer:
the answers is =-0
Step-by-step explanation:
is -0
help help help with maths please
Answers
B. 9cm.
C.9cm.
D. I am not sure sorry
Find the Area of the figure below, composed of a rectangle and a semicircle. The
radius of the circle is shown. Round to the nearest tenths place.
13
3
Answers
Answer:
What grade math is this??
Step-by-step explanation:
Answer:92.1
Step-by-step explanation:
A=78+4.5
A=92.137166941154
A=92.1
cot²3x - 3cot3x +2 = 0
cotx = t
what equation for t
Answers
Answer:
Step-by-step explanation:
cot²(3x)=y
y²-3y+2=0
y²-y-2y+2=0
y(y-1)-2(y-1)=0
(y-1)(y-2)=0
y=1,y=2
cot3x=1
tan 3x=1=tan (π/4)=tan (nπ+π/4)
3x=nπ+π/4=(4nπ+π)/4=(4n+1)π/4
x=(4nπ+1)π/12,n is an integer.
cot 3x=2
tan 3x=1/2
3x=tan^{-1}(1/2)≈26.57°+360n
x≈8.86°+120n
the most obese countries in the world have obesity rates that range from 11.4% to 74.6%.
a. what is the best estimate of the average obesity percentage for these countries?
b. The United States has an average obesity rate of 33.9%. Is this the rate above average or below?
c. How does the United States Compare to other countries?
Answers
The required a) average is 43%, b) average obesity of the United States is below the average, and c) the United States obesity is moderate.
Statistics is the study of mathematics that deals with relations between comprehensive data.
Here,
a. To determine the best estimate of the average obesity percentage for these countries.
Average = 11.4 + 74.6 / 2 = 86 / 2 = 43%.
b. The United States has an average obesity rate of 33.9%.
Since the average is 43%, so the rate of the united states is below the average.
c. How does the United States Compare to other countries?
Since the rate of obesity of the united states is moderate it lies between the interquartile ranges.
Thus, the required a) average is 43%, b) average obesity of the United States is below the average, c) the United States obesity is moderate.
Learn more about Statistics here:
https://brainly.com/question/23091366
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Help please like please
Answers
Answer:
With What?
Step-by-step explanation:
Pls help!! I can’t figure out how to do thisss
Answers
Answer: 30 and 26
Step-by-step explanation:
Please Help Me To Solve For X
Answers
Answer:
u & v = 8
Step-by-step explanation:
This triangle is a special 45-45-90 triangle!
In a 45-45-90 triangle, to solve for the hypotenuse use the formula
[tex]h=(sidelength)*\sqrt{2}[/tex]
Here we see that 8 is being multiplied by radical 2!
We can prove that 8 is the side length by using the Pythagorean Theorem!
find the composition of transformations that map pqr to p'q'r translate, somebody help!?
Answers
Answer:
Translate 2 unit(s) to the right and then reflect over the x-axis
Step-by-step explanation:
You have to move the coordinates of P, Q, and R to the right by 2 so just add 2 to the x coordinate in order to to the first part of the transformation.
After that flip it so that y coordinate of the points are negative to the position they were after translating to the right.
After translating two units to the right, reflect over the x-axis.
What is translation in mathematics?A transformation known as a translation involves shifting each point in a figure by the same amount and in the same direction. For instance, this transformation shifts the parallelogram 3 units upward and 5 units to the right. The formula is (x, y) →(x + 5, y + 3).
Given
Simply add 2 to the x coordinate to complete the first phase of the transformation since you must move the coordinates of P, Q, and R to the right by 2.
Then reverse it so that the points' y coordinates are opposite to where they were before being translated to the right.
To learn more about translation refer to:
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CAN SOMEONE HELP ME WITH THIS PLEASE AND THANK YOU.
Answers
Answer:
17 1/2
Step-by-step explanation:
Please help me with this word problems no files just type it in
Answers
Answer:
40 Dollars!
Step-by-step explanation:
$8 x 5 people = 40!
Match each formula to what it measures.
1. 2 l + 2 w
surface area of a cylinder
2. Πr2
area of a circle
3. 2 Πr2 + 2 Πrh
perimeter of a rectangle
4. Bh
volume of a triangular prism
Answers
Answer:
1. 2l + 2w
Perimeter of a rectangle
2. πr2
Area of a circle
3. 2πrh+2πr^2
Surface area of a cylinder
4. Bh
Volume of a triangular prism.
(This formula means the area of the base multiplied by the height)
Step-by-step explanation:
I really hope this helps!
What is the answer. Do anything begging for help
Answers
Answer:what’s the question?
Step-by-step explanation:
simplify this 2x - 1 = 8
Answers
Answer is below. Look at the steps to clearly understand my answer.
Now, the first time to simplifying this to add both sides by 1.
2x - 1 = 8 → 2x - 1 + 1 = 8 + 1
Since we added both sides, we'll now simplify the problem.
Add both numbers.
2x - 1 + 1 = 2x8 + 1 = 92x = 9Lastly, we'll divide both sides of the equation by the same term.
2x = 9[tex]\frac{2x}{2} =\frac{9}{2}[/tex]Now, cancel both terms that are in both the numerator and denominator.
If you look back at the fraction, 2 is in the numerator and denominator, so we'll cancel those terms.
When you cancelled the terms, you should get x = 9/2.
Any questions? Comment below.
Answer:
Hi, there the answer is [tex]x=\frac{9}{2}[/tex]
Step-by-step explanation:
Step 1: Add 1 to both sides.
2x−1+1=8+1
2x=9
Step 2: Divide both sides by 2.
2x /2 = 9 /2
x= 9 /2
Hope This Helps :)
m∠=6, m∠=+20, and m∠=40+3. List the sides of △ in order from shortest to longest.
Answers
Answer:
m∠=6, ,m∠=+20,m∠=40+3
the larger the angle, the larger the side
The area of a rectangle is represented by the polynomial 3x3+14x2-23x+6. The width of the rectangle is represented by the expression x+6. Find the expression that represents the length of the rectangle.
Answers
Answer:
[tex]l=3x^2-4x+1[/tex]
Step-by-step explanation:
Given that,
The area of a rectangle is, [tex]A=3x^3+14x^2-23x+6[/tex]
The width of the rectangle, b = (x+6)
We need to find the expression for the length of the rectangle. We know that, the area of a rectangle is given by :
A = lb
Where
l is the length of the rectangle
Put all the values,
[tex]l=\dfrac{A}{b}\\\\l=\dfrac{3x^3+14x^2-23x+6}{(x+6)}\\\\l=\dfrac{(x-1)(x+6)(3x-1)}{(x+6)}\\\\l=(x-1)(3x-1)\\\\=3x^2-4x+1[/tex]
So, the length of the rectangle is equal to [tex]3x^2-4x+1[/tex].
A question about the sequence.
Answers
4(x+3) +m(x+3)
Please factorize
Answers
Answer:
4x+12+mx+3m
You use the FOIL method.
Answer:
(4+m)(x+3)
Step-by-step explanation:
x+3 is a common factor, so you can convert this to put the other 2 parts in a bracket. This results in (4+m)(x+3).
An example of how this works is if you made m=1 and x=2. This would make the original expression 4(2+3)+1(2+3), or 4×5+1×5, which is 5×5 or 25. (1+4)(2+3) also equals to 5×5.
**You may want to revise factorising algebraic equations. I'm always happy to help!
Select all of the expressions which show how to convert 2.5 yards into inches.
Answers
Answer:
90
Step-by-step explanation:
A tablet and a digital camcorder are both on sale for 30% off. The regular price of the tablet is $185. The regular price of the camcorder is $140.
Answers
Answer:
355
Step-by-step explanation:
185+140= 325
325+20= 355
Answer:
30/185×100=
Step-by-step explanation:
30/140×100=
48. Determine whether the given measurements determine 0, 1, or 2
possible triangles.
a=19.3, c= 21.9, C = 39.4°
Answers
Answer:39.9
Step-by-step explanation:
EASY GEOMETRY PLS HELP!!!! AREA IF parallelogram
Answers
Answer
80 m^2
Step-by-step explanation:
basically 10 x 8 plus the value
Tina, a single woman, earned wages of $70549, received $1287 in interest from a savings account, and contributed $2753 to a tax-deferred saving plan. She contributed $1505 to charity. Find Tina's federal tax. (More info in the attachment)
Answers
Answer:
[tex]\$14,733.25[/tex]
Step-by-step explanation:
Taxable income refers to the income subject to taxes from government, including but not limited to federal tax.
Since taxable income is equal to $58,933, tax will be based off of this value. Because Tina is single and her income falls within the 25% range, her federal tax is equal to:
[tex]\$58,933\cdot 0.25=\boxed{\$14,733.25}[/tex]
The graph of h (x) = StartAbsoluteValue x minus 10 EndAbsoluteValue + 6 is shown. On which interval is this graph increasing
Answers
Answer:
x≥10 or x∈[10, ∞)
Step-by-step explanation:
The graph we are given is h(x) = |x-10|+6, which has the shape of a V. The vertex is at (10, 6), so to the right of the vertex, the graph is increasing.
Therefore, the graph increases during the interval x≥10 or x∈[10, ∞).
Bradley is preparing a presentation to show the CEO of his company. He wants to emphasize that the profits of their competitor have increased slowly over the past 16 months.
Answers
Answer:
(1) Graph A
(2) Appears to increase less
Step-by-step explanation:
Given
See attachment for complete question
Required
Complete the blanks
The graph to use and why?
From the question, we understand that he wants to present the graph with lower increment of profit.
By comparing graphs A and B, we can see that graph A appears to have a slow increment with month, while B has a higher rate of increment.
Hence, he should use graph A
Which set is closed under subtractionWhich answer choice shows that the set of irrational numbers is not closed under addition
Answers
Answer:
(a) Set of rational numbers
(b) [tex]\pi + (-\pi) = 0[/tex]
Step-by-step explanation:
Solving (a): Set that is closed under subtraction
The solution to this is rational numbers.
For a set of number to be closed under subtraction, the following condition must be true
[tex]a -b = c[/tex]
Where
a, b, c are of the same set.
The above is only true for rational numbers.
e.g.
[tex]1 - 2 = -1[/tex]
[tex]5 - 5 = 0[/tex]
[tex]\frac{1}{2} - \frac{1}{4} = \frac{1}{2}[/tex]
[tex]4 - 2 = 2[/tex]
The operations and the result in the above samples are rational numbers.
Solving (b): Choice not close under addition[See attachment for options]
As stated in (a)
For a set of number to be closed under subtraction, the following condition must be true
[tex]a -b = c[/tex]
Where
a, b, c are of the same set.
In the given options (a) to (d), only
[tex]\pi + (-\pi) = 0[/tex] is not close under addition because:
[tex]\pi[/tex] is irrational while [tex]0[/tex] is rational
In other words, they belong to different set
What is the sum of the exterior angle measures for a regular hexagon?
Answers
Answer:
Answer is 360
to find each of the angles take 360 ÷ by the number of sides , in this case is 360 ÷ 6 = 60
Answer:
Option D is correct
Step-by-step explanation:
Sum of exterior angle measures for a regular hexagon = 360°
Hope it is helpful...Can someone help me out these problems !!!
Answers
Answer:
Zoom in more and I can help
Step-by-step explanation:
I NEED HELP PLEASE UHHH PLEASE I NEED HELP UUUUHHHHHHH
Sulio wants to build a wooden fence to enclose his vegetable garden. Determine the amount of fencing he needs by finding the perimeter of the garden.
Perimeter = 2 times length + 2 times width. The length of a garden is 8 feet and the width is 6 feet.
Evaluate the formula for the perimeter of a parallelogram to solve the problem. Then check all that apply.
First, write the formula for the perimeter of a parallelogram, P = 2l + 2w.
Next, use parentheses when you substitute 8 for l and 6 for w.
After multiplying, add 16 and 12.
Sulio needs 28 feet of fencing.
Sulio needs 48 feet of fencing.
Answers
Answer:
Sulio needs 28 feet of fencing
Step-by-step explanation:
P= 2l + 2w
Length- 8 ft
Width- 6 ft
Use formula with the given:
2(8) + 2(6)
= 16 + 12
= 28
Therefore, Sulio needs 28 feet of fencing
Hope this helps
Answer:
a, b, c, d
Step-by-step explanation:
A woman buys a pair of shoes at a sale,
She pays $60. saving $15 on the regular
price. The percentage discount on the
shoes is
(A)
20
(B)
25
-
(C)
33
3
(D)
80
Answers
Answer:
20 %
Step-by-step explanation:
If she saved 15 dollars and paid 60, the original price was 60+15 = 75
The percent discount is (original - new) / original = ( 75-60)/75 = 15/75 = .2
Change to percent form = .2 * 100 =20%
Answer:
B.) 20 %
The percentage discount on the shoes is 20 % .
Step-by-step explanation:
Given :- A woman buys a pair of shoes at a sale . She paid $60 and saving $15 on the regular price.To Find :-The percentage discount on the shoesSolution. :-She pays 60 dollers and saved 15 dollers on the regular price.
original price of pair of shoes = 60 + 15 = 75
Percentage discount is = original price - new price / original price
= 75 - 60 / 75 = 15 / 75 = 0.2
Percentage discount = 0.2
Change into percentage =0.2× 100 = 20%
Therefore, the percentage discount on the shoes is 20 % .
