**PLEASE HELP I NEED IT WITHIN 20 MINUTES**
These are Trig Ratios and you can read the instructions to solve question 15 & 16 (if you can please show the work it would be greatly appreciated)
Answers
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions[1][2]) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena, through Fourier analysis.
Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their side lengths are proportional. Proportionality constants are written within the image: sin θ, cos θ, tan θ, where θ is the common measure of five acute angles.
The trigonometric functions most widely used in modern mathematics are the sine, the cosine, and the tangent. Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used. Each of these six trigonometric functions has a corresponding inverse function (called inverse trigonometric function), and an equivalent in the hyperbolic functions as well.[3]
The oldest definitions of trigonometric functions, related to right-angle triangles, define them only for acute angles. To extending these definitions to functions whose domain is the whole projectively extended real line, geometrical definitions using the standard unit circle (i.e., a circle with radius 1 unit) is often used. Modern definitions express trigonometric functions as infinite series or as solutions of differential equations. This allows extending the domain of sine and cosine functions to the whole complex plane, and the domain of the other trigonometric functions to the complex plane (from which some isolated points are removed).
Contents
Right-angled triangle definitions Edit
A right triangle always includes a 90° (π/2 radians) angle, here labeled C. Angles A and B may vary. Trigonometric functions specify the relationships among side lengths and interior angles of a right triangle.
Plot of the six trigonometric functions, the unit circle, and a line for the angle θ = 0.7 radians. The points labelled 1, Sec(θ), Csc(θ) represent the length of the line segment from the origin to that point. Sin(θ), Tan(θ), and 1 are the heights to the line starting from the x-axis, while Cos(θ), 1, and Cot(θ) are lengths along the x-axis starting from the origin.
In this section, the same upper-case letter denotes a vertex of a triangle and the measure of the corresponding angle; the same lower case letter denotes an edge of the triangle and its length.
Given an acute angle A = θ of a right-angled triangle, the hypotenuse h is the side that connects the two acute angles. The side b adjacent to θ is the side of the triangle that connects θ to the right angle. The third side a is said to be opposite to θ.
If the angle θ is given, then all sides of the right-angled triangle are well-defined up to a scaling factor. This means that the ratio of any two side lengths depends only on θ. Thus these six ratios define six functions of θ, which are the trigonometric functions. More precisely, the six trigonometric functions are:[4][5]
sine
{\
Related Questions
Given f(x) = 2x^3 + ax^2 - 7a^2x - 6a^3, determine whether or not x-a and x+a are factors of f(x). Hence, find, in terms of a, the roots of f(x) = 0.
thankyou so much
Answers
Answer:
Step-by-step explanation:
f(x) = 2x³ + ax² - 7a²x - 6a³
= 2x³ - 2a²x + ax² - a³ - 5a²x - 5a³
= 2x(x² - a²) + a(x² - a²) - 5a²(x+a)
= (2x+a)(x - a)(x + a) - 5a²(x + a)
= (x + a)[(2x + a)(x - a) - 5a²]
= (x + a)(2x² - ax - 6a²)
= (x + a)(2x + 3a)(x - 2a)
x-a is the factor of the equation and x + a is not a factor of the equation,
All the roots of the equation are x + a, 2x+3a, x-2a.
What is a cubic equation ?"In algebra, a cubic equation in one variable is an equation of the form
ax^3+bx^2+cx+d=0
in which a is nonzero.
The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients a, b, c, and d of the cubic equation are real numbers, then it has at least one real root (this is true for all odd-degree polynomial functions). "
Given equation is [tex]f(x) = 2x^3 + ax^2 - 7a^2x - 6a^3[/tex]
Now,
[tex]f(x) = 2x^3 + ax^2 - 7a^2x - 6a^3\\\\= 2x^3 - 2a^2x + ax^2 - a^3 - 5a^2x - 5a^3\\\\= 2x(x^2 - a^2) + a(x^2 - a^2) - 5a^2(x+a)\\\\= (2x+a)(x - a)(x + a) - 5a^2(x + a)\\\\= (x + a)[(2x + a)(x - a) - 5a^2]\\\\= (x + a)(2x^2 - ax - 6a^2)\\\\= (x + a)(2x + 3a)(x - 2a)[/tex]
Hence, the roots of the equation are x + a, 2x +3a, x - 2a.
To know more about cubic equation here
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Ricky and Sam each bought a remote control car for $80. A few months later they both sold it. Ricky sold his car for 25% less than the original price and Sam sold his car for 30% less than the original price. How much more did Ricky get than Sam?
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Answer:
Ricky get $4 than Sam.
Step-by-step explanation:
.25x80=20
80-20=60
.30×80=24
80-24=56
Is this true or false? Ill give brainliest!!!
Answers
Answer:true
Step-by-step explanation:
A biker cycles 9 miles in 2 3 of an hour.
a
Make a chart and fill it in to show how far he will bike if he maintains the same pace for 2 hours, 3 hours, 3.5 hours
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Answer:
2 hours: 27 miles, 3 hours: 40.5 miles, 3.5 hours: 47.25 miles
Step-by-step explanation:
1.) If a hiker hikes 9 miles in 2/3 of an hour, he will hike 4.5 (Half of 2/3 is 1/3 and half of 9 is 4.5) miles in 1/3 of an hour and 13.5 miles per hour. (1/3 times 3 gives us a whole and 4.5 times 3 is 13.5)
2.) 2 hours: 13.5 * 2 = 27 miles
3.) 3 hours: 13.5 * 3 = 40.5 miles
4.) 3.5 hours: 13.5 * 3.5 = 47.25 miles
2 hours: 27 miles, 3 hours: 40.5 miles, 3.5 hours: 47.25 miles
Step-by-step explanation:
1.) If a hiker hikes 9 miles in 2/3 of an hour, he will hike 4.5 (Half of 2/3 is 1/3 and half of 9 is 4.5) miles in 1/3 of an hour and 13.5 miles per hour. (1/3 times 3 gives us a whole and 4.5 times 3 is 13.5)
2.) 2 hours: 13.5 * 2 = 27 miles
3.) 3 hours: 13.5 * 3 = 40.5 miles
4.) 3.5 hours: 13.5 * 3.5 = 47.25 miles
this is the guys above i just need points
PLEASE HELP ME 18 POINTS PLEASE HELP
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Answer:
the y-intercept it at 3
Answer:
(3,0) !
Step-by-step explanation:
The y intercept is where the given line touches the y axis (the vertical line of a coordinate plane)
I hope this helps!
Please dont steal points. i will report.
Answers
Answer:
C.
Hope this helps.
have a good one
Jaxon invested $58,000 in an account paying an interest rate of 2.7% compounded
quarterly. Assuming no deposits or withdrawals are made, how much money, to the
nearest dollar, would be in the account after 14 years?
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Answer:
A≈84536
Step-by-step explanation:
After 14 year span, the money in the account would be $84,535.62.
Given that,
Jaxon invested $58,000 in an account paying an interest rate of 2.7% compounded quarterly.
Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.
Here,
principal(P) = 85000
rate(r) = 2.7% = 0.027
Time(a) = 14 years,
n = 4
Apply compound interest identity,
Amount = principal[1 + r/n]ⁿᵃ
Amount = 58000[ 1 + 0.027/4]⁴ˣ¹⁴
Amount = 84,535.62
Thus, After a 14-year span, the money in the account would be $84,535.62.
Learn more about compound interest here:
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Im Giving Brainliest............. Someone Plzz Help?
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Answer:
For the first one 25.925%
The second is 23.333%
The third is 27.27%
Let me know if this helps!
2x + y = -8
3x - 5y = -25
It’s substitution
Answers
Answer:
x = -5 , y = 2
Step-by-step explanation:
Solve the following system:
{y + 2 x = -8
-5 y + 3 x = -25
Hint: | Choose an equation and a variable to solve for.
In the first equation, look to solve for y:
{y + 2 x = -8
-5 y + 3 x = -25
Hint: | Solve for y.
Subtract 2 x from both sides:
{y = -2 x - 8
-5 y + 3 x = -25
Hint: | Perform a substitution.
Substitute y = -2 x - 8 into the second equation:
{y = -2 x - 8
3 x - 5 (-2 x - 8) = -25
Hint: | Expand the left hand side of the equation 3 x - 5 (-2 x - 8) = -25.
3 x - 5 (-2 x - 8) = (10 x + 40) + 3 x = 13 x + 40:
{y = -2 x - 8
13 x + 40 = -25
Hint: | Choose an equation and a variable to solve for.
In the second equation, look to solve for x:
{y = -2 x - 8
13 x + 40 = -25
Hint: | Isolate terms with x to the left hand side.
Subtract 40 from both sides:
{y = -2 x - 8
13 x = -65
Hint: | Solve for x.
Divide both sides by 13:
{y = -2 x - 8
x = -5
Hint: | Perform a back substitution.
Substitute x = -5 into the first equation:
{y = 2
x = -5
Hint: | Sort results.
Collect results in alphabetical order:
Answer: {x = -5 , y = 2
Which of the tables represents a function? Table AInput Output 4 3 3 2 3 1 Table BInput Output 1 3 3 5 5 7 Table CInput Output 0 0 1 4 1 5 Table DInput Output 4 1 4 2 4 3 Table A Table B Table C Table D
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Answer:
The answer is Table B. Because only table B. doesn't have repeating x or domain.
Answer:
I think the answer might be b
Step-by-step explanation:
Please answer !!!!!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
<A = 117degrees
Step-by-step explanation:
<A and <B are verticle angles, as given. Hence they will be of equal measures. It is given that <A = 5x -3, and <B = 4x + 21.
Using this, set up an equation;
<A = <B
5x - 3 = 4x + 21
Inverse operations,
5x - 3 = 4x + 21
+3 +3
5x = 4x + 24
-4x -4x
x = 24
Now substitute back in, to find the measure of <A,
5x - 3
x = 24
5 ( 24 ) - 3
120 - 3
117
PLZZZZ HELPPPPP!! THIS IS TIMED!!
Find the length of MN.
*LOOK AT PICTURE*
Answers
Answer:
MN = 10
Step-by-step explanation:
There is a scale factor of 2 [This means that the lengths of triangle ∆MPN are exactly 2 times larger than ∆SRQ], so 5 × 2 = 10.
Notice that each corresponding line is marked by a black mark perpendicular to the side. Since 2 corresponds to 4, and 3 corresponds to 6, 5 must correspond to 10. These triangles are similar as indicated by the marks so there is just a size difference. Because these two triangles are similar, the sides must be proportional.
∆MPN ~ ∆SRQ.
It can also be thought of as completing a set of proportional fractions:
4/2 = 6/3 = ?/5
4/2 = 2 → 6/3 = 2 → ?/5 = 2.
?/5 = 2, ? = 5 × 2 = 10.
Find the value of 2 - 3x when x = 7 PLEASE HELP ME :(
Answers
Answer:
-19
Step-by-step explanation:
Answer:
-19
Step-by-step explanation:
replace x with seven then simplify
please help! algebra 1
Answers
(y2 - y1) / (x2 - x1)
(-10 - (-4)) / (-12 - (-20))
= -6/8
Therefore the answer is D.
write an equivalent expression by distributing the "_" sign outside the parenthesis
1.6n-(4p-3)
Answers
9514 1404 393
Answer:
1.6n -4p +3
Step-by-step explanation:
Distributing the minus sign changes the signs of all the terms inside parentheses.
-(4p-3) = -4p +3
When that is added to 1.6n, the entire expression is ...
1.6n -4p +3
PLS HELP ITS DUE IN AN HOUR!
WILL GIVE BRAINLIEST!
Answers
Answer:
Step-by-step explanation:
Unfortunately other people have promised to give Brainliest before and they never did. However, I'll answer the third question and tell you that it's 8 sides.
Solve this equation algebraically!!!
Answers
Answer:
See Explanation
Step-by-step explanation:
[tex]1 - \sqrt{x} \neq \: 0 \\ \\ \therefore \: 1 \neq \sqrt{x} \\ \\ {1}^{2} \neq ({ \sqrt{x}) }^{2} \\ \\ 1 \neq \: x \\ [/tex]
Hence, x will take values other than 1.
The perimeter of a rectangular parking lot is 312m .
If the length of the parking lot is 95 m, what is its width?
Answers
Answer:
61 meters
Step-by-step explanation:
The perimeter of a rectangle is 2l + 2w, l being the length and w being the width. Substitute the known value into the equation and solve:
312 = 2(95) + 2w
312 = 190 + 2w
122 = 2w
w = 61
PLZ HELP QUICK Which property explains why these two expressions are equal - the commutative, the associative, or distributive property of addition?
1 + (2 + 3) = (1 + 2) + 3
Answers
Answer:
I think it's commutative. ;-;
Step-by-step explanation:
2-90 Frieda Friendly works for a local car dealership. She noticed that 3434
34
of the cars are sedans and that half of them are white. What fraction of the dealership’s cars are white sedans?
A. Use a unit rectangle to represent this situation. Label the parts carefully. (Complete in your notebook.)
B. Write an equation or a sentence that describes the situation, and answer the question. (Complete in your notebook.)
Write your answer from part (b) as a decimal and as a percent.
PLEASE ISTG IM CRYING OVER THIS QUESTION- I'LL MARK BRAINLIEST!!!!!!
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please complete the chart with the correct angle measures
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Answer:
10. X= 11
11. X= 5
Step-by-step explanation:
5x-8+43=90
x= 11
--------------------
3x+3+72=90
x= 5
give brainliest pls
common difference for 7,15,23,31,29
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Answer: it’s 8 if that 29 is supposed to be a 39 otherwise i don’t know
Step-by-step explanation:
About how many $40 shirts could you buy with $290?
Answers
Answer:
7 shirts
Step-by-step explanation:
290/40 = 7.25
But since you can't have 7.25 shirts, it's just 7.
The graph of a function f is shown. Use the graph to estimate the average rate of change from x=-2 to x=0
Answers
Answer:
2
Step-by-step explanation:
Given:
The interval, x = -2 to x = 0.
Required:
Average rate of change from x = -2 to x = 0.
SOLUTION:
From the graph,
If x = -2, f(-2) = 0.
If x = 0, f(0) = 4
Average rate of change = [tex] \frac{f(b) - f(a)}{b - a} [/tex]
Where,
[tex] a = -2, f(a) = 0 [/tex]
[tex] b = 0, f(b) = 4 [/tex]
Plug in the values into the formula:
[tex] = \frac{4 - 0}{0 -(-2)} [/tex]
[tex] = \frac{4}{2} = 2 [/tex]
Average rate of change from x = -2 to x = 0 is 2.
pls help me with this
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Error: She did not fully simplify [tex]\sqrt{12x^{3}}[/tex]
Correct simplification:
[tex]5x\sqrt{48x^{5}}\\\\=5x\sqrt{16x^{4}}\sqrt{3x}\\\\=5x(4x^{2})\sqrt{3x}\\\\=20x^{3}\sqrt{3x}[/tex]
Aubrey bought 5 packs of stickers each with 30 stickers. Izzy bought 4 packs,
each with 40 stickers. How many stickers do they have total
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They have 310 stickers in total
Okay yes I know it's messy it was a long stressful day lol so just check the last two, are they written right? are they even right? Thanks so much love you guys!!!!!!
Answers
Answer:
Yes
Step-by-step explanation:
Yes it is
No 1 is correct
No 2 is correct
No 3 is correct
No 4 is correct
and what i mean by correct is you answered it correct
I hope this helps you :)
Answer:
yes
Step-by-step explanation:
yes it is
it is all correct
A pie recipe calls for u to use 3/8 cup of milk, 1/8 cup of oil, and 3/8 cup of water. How many liquid do you need to make the pie
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At the time that a 55 foot tall tree casts a shadow that is 32 feet long, a nearby woman is 5.5 feet tall. Which measure is the closest to the length of the shadow she will cast?
Answers
Answer:
3.2ft long shadow
Step-by-step explanation:
In this problem we are given a ratio between the tree/shadow and woman/shadow therefore we are given 3 values and 1 unknown then we can use the Rule of Three to calculate the length of the shadow which we will refer to as x. The Rule of Three simply multiplies the diagonal values and divides by the third value in order to get the missing unknown like so...
55ft tall <======> 32ft long shadow
5.5ft tall <======> x ft long shadow
(5.5 * 32) / 55 = 3.2ft long shadow
Finally, we can see that the woman's shadow would be a 3.2ft long shadow
help me please , the question is in the picture .
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Answer: 4.2x10^5=420000
Step-by-step explanation: its a positive five so you go in the positive direction from the decimal but if it was a negative you could go the other way (hope this helps)
