how to define trigonometric ratios
Answers
[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]
Formula for trignometric ratios.[tex] \huge \boxed{\mathfrak{Answer} \downarrow}[/tex]
The trignometric ratios are [tex]\downarrow[/tex][tex]\downarrow[/tex]
[tex]\begin{gathered}\begin{gathered}\begin{array}{||c|c|c||} \\ \rm sin \: A & \dfrac{\sf\:Opposite\: side\: of\: angle\: A }{\sf\:Hypotenuse \: } & \dfrac{\sf\:BC}{\sf\:AC} \\ \\ \rm cos \: A & \dfrac{ \sf\: Adjacent \:side \:of\: angle \:A }{\sf\: Hypotenuse} & \dfrac{\sf\: AB}{ \sf\: AC} \\ \\ \rm tan A & \dfrac{\sf\: Opposite \:side \:of \:angle\: A}{ \sf\: Adjacent \:side \:of \:angle \:A } & \dfrac{\sf\:BC}{ \sf\: AB}\\ \\ \rm cosec A & \dfrac{\sf\: Hypotenuse}{\sf\: Opposite\: side \:of\: angle\: A}& \dfrac{\sf\:AC}{ \sf\:BC } \\ \\ \rm sec A & \dfrac{\sf\: Hypotenuse}{ \sf\: Adjacent \:side\: of\: angle \:A}& \dfrac{\sf\:AC}{\sf\:AB}\\ \\ \rm cot A & \dfrac{\sf\: Adjacent \:side\: of \:angle \:A}{\sf\: Opposite\: side \:of\: angle\: A} & \dfrac{\sf\:AB}{ \sf\: BC} \end{array}\end{gathered}\end{gathered} \\ \\ - \bf \: Lucazz \: (brainly.com)[/tex]
Refer to the picture for better understanding.
Related Questions
you buy 12 apples. you also buy a box of cereal for $3.35. the bill is 8.75. how much does each apple cost
Answers
Total 12 apple = $5.40
I got this by
8.75-3.35=5.40
5.40/12
Each apple cost $0.45
Working together , 5 friends collected 40 5/8 bags of food for the homeless . On a average how many bags of food did each friend collect ?
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Mr. Welch bought 24 ft of fencing.
How many yards of fencing did he buy? (1 yd = 3 ft)
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1 yard = 3 feet
divide 24 feet by 3 feet to get yards
24 / 3 = 8 yards
the exact radius of a circle with circumference 36 meters
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There is 1/4 ounce of yeast in every 2 and 1/4 teaspoons of yeast. A recipe for bread calls for 2 teaspoons of yeast. How many ounces of yeast are needed for this recipe?
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what is -5x + 2 equals negative 48
Answers
First you would subtract 2 to -48 and that gives you -50. After you will divide the -5x to -50 and that gives you X=10
The Hamptons family has a fish tank holding 10,450 ml of water.The water is leaking at a rate of 270 ml per minute.
Part A: Define the input and output in the given scenario.
Part B: Write a function to model this situation.
Part C: How many liters of water will be left in the tank after 10 minutes.?
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B: f(x)=10450-270x
C: f(10)=10450-270(10)=7750 ml of water
We can give a letter 't' for the time, the input, and f(t) for the output
----------------------------------------------------------------------------------------------------------------
The original amount of water in the tank is 10450, so this will be the fixed constant.
The amount of water lost per minute is 270 so this will be the term that varies depends on the variable of time, we write this as 270t
The function is given f(t) = 10450 - 270t
--------------------------------------------------------------------------------------------------------------
Given, t = 10
f(10) = 10450 - 270(10)
f(10) = 7750 ml
The amount of money Kelly earns is proportional to the number of hours she works. Kelly earns $32.40 working 4 hours. Create an equation that models the relationship between the amount of money Kelly earns, in dollars, and h, the number of hours she works.
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y = 8.10h...where y is the amount of money earned and h is the number of hrs worked
PLEASE HELP ME.
Show Work.
Use two unit multipliers to convert 70 meters to inches.
Answers
.
Rough check, 1 m = 39.36 in approx , 70*39.36 = 2755.2
I think that's how it's done. As far as explaining it goes, I can't do that. I had to ask my math teacher and she wrote the calculations down.
To convert 70 meters to inches, use the unit multiplier method. 70 meters is equal to 2755.91 inches.
Explanation:To convert meters to inches, we can use the unit multiplier method. There are two unit multipliers we can use:
1 meter = 39.37 inches and 1 inch = 0.0254 meters.
Start with the given quantity of 70 meters.Multiply by the unit multiplier 39.37 inches / 1 meter. This will cancel out the meters and leave us with the equivalent value in inches.Multiply the result by the unit multiplier 1 meter / 0.0254 inches. This will cancel out the inches and convert the value back to meters.Simplify the expression to find the final answer.Therefore, 70 meters is equal to 2755.91 inches.
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An aquarium with a square base has no top. There is a metal frame. Glass costs 8 dollars/m^2 and the frame costs 7 dollars/m. The volume is to be 20 m^3. Express the total cost C in terms of the height h in meters. (Hint: work out the cost of the glass and frame separately.)
Answers
Volume = Area of Base x height
Area of Base = Volume / height = 20/h
Given that the aquarium has a square base.
Area of square = l^2
Thus, the length of the base of the aquarium is [tex] \sqrt{area \ of \ base} = \sqrt{ \frac{20}{h} } [/tex]
The frame is to cover 8 sides with the length equal to the length of the base and 4 sides with the length of the height.
Thus, the total perimeter of the frame is given by [tex]8\sqrt{\frac{20}{h}}+4h= \sqrt{64\left(\frac{20}{h}\right)}+4h = \sqrt{\frac{1,280}{h}}+4h [/tex]
Area of the four side faces of the aquarium is 4 times the length of the base times the height = [tex]4\times\sqrt{ \frac{20}{h} }\times h=\sqrt{16\left(\frac{20}{h}\right)h^2}=\sqrt{320h}[/tex]
Total area to be covered by grass is the base and the four side faces and is given by [tex]\frac{20}{h}+\sqrt{320h}[/tex]
Cost of the entire metal frame = [tex]7\left(\sqrt{\frac{1,280}{h}}+4h\right)= \sqrt{49\left(\frac{1,280}{h}\right)}+7(4h) = \sqrt{\frac{62,720}{h}}+28h [/tex]
Cost of the entire grass = [tex]8\left(\frac{20}{h}+\sqrt{320h}\right)=\frac{160}{h}+\sqrt{64(320h)}=\frac{160}{h}+\sqrt{20,480h[/tex]
Therefore, total cost in terms of the height, h, is given by
[tex]C=\sqrt{\frac{62,720}{h}}+28h+\frac{160}{h}+\sqrt{20,480h[/tex]
Which show another way to write the ratio 13:9 ?
Answers
26:18 (x2 to both)
39:27 (x3 to both)
hope this helps
Bruno's hourly salary is 6.75. Last Week he worked a 20 hour week. How Much did he earn
Answers
Bruno makes 6.75 per hour that can be represented by the following; h being the variable for "hours" hence, the h.
6.75h
Las week he worked 20 hours, so plug that in for h
Like so ;
6.75(20) = How much $ Bruno made
135 = how much $ Bruno made
So Bruno made 135$ last week.
find the rate of change for 2x+4y=10
Answers
rate of change for 2x+4y=10
here rate of change can be found by finding slope
the general form for slope is y=mx+b
isolating y on the left side:
2x+4y=10
4y=[tex] y=\frac{-2x+10}{4}
[/tex]-2x+10
from here slope is -1/2
Rate of change =-1/2
Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 7 liters of natural oil for every 5 liters of synthetic oil. If 355 liters of synthetic oil are used, how many liters of petrolyn oil will be made?
Answers
Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 7 liters of natural oil for every 5 liters of synthetic oil.
What we need to find:
If 355 liters of synthetic oil are used, how many liters of petrolyn oil will be made?
Set up a proportion to find how much natural oil is used.
7L natural oil/5L synthetic oil = x/355 synthetic oil where x=natural oil
7/5=x/355
(5)(x)=(7)(355) cross multiplied
5x=2485 simplified
5/5x=2485/5 multiplicative inverse
x=497L
Now, add both synthetic oil and natural oil to find amount of petrolyn oil.
355 L synthetic oil + 497 L natural oil= 852 L of petrolyn oil
PLEASE HELP 30 points!!!!
what is the slope of this line in the picture?
Answers
because the answer 3/12 = 1/4
-4.2 (-2.8+4.5) what is the value of the expression
Answers
Use the sequence below to answer parts a and b (8,17,26,35,44,53,...) Create an explicit formula to determine the 12th term of the sequence Create a recursive formula to prove the 7th term is 62.
Answers
The explicit formula for the sequence (8, 17, 26, 35, 44, 53, ...) is 8 + (n-1) * 9, and the 12th term can be found by substituting n = 12. The recursive formula for the sequence is a1 = 8 and an = an-1 + 9. Using this recursive formula, we can verify that the 7th term is indeed 62.
Explanation:To create an explicit formula for the sequence (8, 17, 26, 35, 44, 53, ...), we notice that the difference between each term is 9. So, the explicit formula for the sequence is 8 + (n-1) * 9, where n represents the position of the term in the sequence. Using this formula, we can find the 12th term by substituting n = 12: 8 + (12-1) * 9 = 89.
To create a recursive formula to prove that the 7th term is 62, we observe that each term is the previous term plus 9. So, the recursive formula for the sequence is:
a1 = 8an = an-1 + 9Using this recursive formula and starting with a1 = 8, we can find the 7th term as follows:
a1 = 8a2 = a1 + 9 = 8 + 9 = 17a3 = a2 + 9 = 17 + 9 = 26a4 = a3 + 9 = 26 + 9 = 35a5 = a4 + 9 = 35 + 9 = 44a6 = a5 + 9 = 44 + 9 = 53a7 = a6 + 9 = 53 + 9 = 62Therefore, the 7th term in the sequence is indeed 62.
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What is the best way to 7x7 in expanded form?
Answers
Answer: Add 7 7 times
Step-by-step explanation: if you add 7 7 times like this 7+7+7+7+7+7+7 then that is your answer easy way too.
(20 points)
What is the perimeter of the figure?
229-4/9 ft
229-2/3 ft
230-2/3 ft
231 ft
Answers
60 5/6 + 56 1/6 = 117
59 1/3 + 54 1/3 = 113 2/3
117 + 113 2/3 = 230 2/3 feet
5 different mixed numbers that add up to 10 with only 3rds and 4ths
Answers
2 2/3
1 2/4
3 1/4
1 1/4
Julia plays volleyball and finished the regular season with 25 digs. The graph relates her total number of digs for the season to the number of games played in the post-season tournament. Graph in the coordinate plane with title Julia’s volleyball digs. Vertical axis goes from 0 to 60 in increments of 5 and is labeled number of digs. Horizontal axis goes from 0 to 10 in increments of 1 and is labeled games played. A ray on the graph starts at point begin ordered pair 0 comma 25 end ordered pair and goes through points begin ordered pair 4 comma 37 end ordered pair and begin ordered pair 8 comma 49 end ordered pair. What is the equation in standard form that represents the relationship shown in the graph? y=3x+25 y−37=3(x−4) 3x+y=25 −3x+y=25 y=−3x+25
Answers
Answer:
As given : Graph in the coordinate plane with title Julia’s volleyball digs. Vertical axis goes from 0 to 60 in increments of 5 and is labeled number of digs. Horizontal axis goes from 0 to 10 in increments of 1 and is labeled games played. A ray on the graph starts at point begin ordered pair 0 comma 25 end ordered pair and goes through points begin ordered pair 4 comma 37 end ordered pair and begin ordered pair 8 comma 49 end ordered pair.
As the ray passes through (0,25) and (4,37) and (8,49).
Equation of line passing through (a, b) and (p,q) is given by:
→ [tex]\frac{y-b}{x-a}=\frac{q-b}{p-a}[/tex]
→Equation of line passing through (0,25) and (4,37) is :
[tex]\frac{y-25}{x-0}=\frac{37-25}{4-0}=3\\\\y -25=3x\\y =3x + 25[/tex]
As , y= 3 x + 25, also passes through (8,49) also.
Equation of line is : y = 3 x + 25 or in Standard form : - 3 x + y = 25
Option (D) is the standard form of line which is : - 3 x + y = 25
Simplify:
4p + 12 – 3q – 4p – 18 + 6q
A. 8p + 3q – 6
B. 8p – 3q + 6
C. 3q + 6
D. 3q – 6
Answers
4p + 12 - 3q - 4p - 18 + 6q
Combine like terms
4p - 4p + 12 - 18 - 3q + 6q
= -6 + 3q
The correct answer is option D
The simplifying value of the expression is,
⇒ 3q - 6
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 4p + 12 - 3q - 4p - 18 + 6q
Now,
Simplify the expression as;
⇒ 4p + 12 - 3q - 4p - 18 + 6q
⇒ 4p - 4p - 3q + 6q + 12 - 18
⇒ 0 + 3q - 6
⇒ 3q - 6
Thus, The simplifying value of the expression is,
⇒ 3q - 6
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the temperature at 6:00AM was 0.8F. BY. 3:00pm the temperature had increased to 2.4 F find the differnce between the two temperatures. Draw models to find the difference
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If there are 1000 grams in a kilogram and 454 grams in a pound, how many pounds are there per kilogram?
Answers
Answer:2.2 pounds per kilogram
Step-by-step explanation:
454gram = 1 pound
since; 1000g = 1kg
454g = x
x= 454/1000
x=0.454kg
there is 0.454kg in 1 pound
but the question says how many pound is in 1kg
0.454kg = 1 pound
1 kg = x
cross multiply
0.454x = 1
Divide bothside by 0.454
x = 1/0.454
x = 2.2 pound
Therefore; there are 2.2pounds in 1 kilogram.
There are 2.20 pounds are there per kilogram
Given that,
1 kg = 1000 gm
1 pound = 454 gm
Since we know that,
A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.
Since,
1 pound = 454 gm
Therefore,
⇒ 454 gm = 1 pound
⇒ 1 gm = 1/454 pound
And since,
1 kg = 1000 gm
= 1000x(1/454) pound
= 2.20 pounds
Hence,
1 kg = 2.20 pounds
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Triangle ABC is dilated with a center at the origin and a scale factor of 2. What are the coordinates of triangle A’B’C’?
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The coordinates of triangle A'B'C' are A'(-4, 4), B'(2, 6) and C'(-2, 0).
Given that, triangle ABC is dilated with a center at the origin and a scale factor of 2.
What is a dilation?Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.
From the given graph, A(-2,2), B(1, 3) and C(-1, 0)
By using a scale factor of 2, we get
A(-2,2)→2(-2, 2)=A'(-4, 4)
B(1, 3)→2(1, 3)=B'(2, 6)
C(-1, 0)→2(-1, 0)=C'(-2, 0)
Therefore, the coordinates of triangle A'B'C' are A'(-4, 4), B'(2, 6) and C'(-2, 0).
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does it matter whether you remove x tiles or 1 tiles first
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Rewrite the expression with parentheses to equal the given value 12+6÷2+4 value 13
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If the equatorial diameter of the sun is 1.39 million km how many kilometers is the sun's radius
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1. What events led to the attack at Pearl Harbor?
I know that this isn't math but I just need help please. :(
Answers
Is 789 a terminating, Repeating, or Non-repeating Decimal?