Answers
Answer:
The trigonometric ratios are presented below:
[tex]\sin \theta = \frac{AC}{\sqrt{AC^{2} + BC^{2}}}[/tex]
[tex]\cos \theta = \frac{BC}{\sqrt{AC^{2} + BC^{2}}}[/tex]
[tex]\cot \theta = \frac{BC}{AC}[/tex]
[tex]\sec \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{BC}[/tex]
[tex]\csc \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{AC}[/tex]
Step-by-step explanation:
From Trigonometry we know the following definitions for each trigonometric ratio:
Sine
[tex]\sin \theta = \frac{y}{h}[/tex] (1)
Cosine
[tex]\cos \theta = \frac{x}{h}[/tex] (2)
Tangent
[tex]\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{y}{x}[/tex] (3)
Cotangent
[tex]\cot \theta = \frac{\cos \theta}{\sin \theta} = \frac{x}{y}[/tex] (4)
Secant
[tex]\sec \theta = \frac{1}{\cos \theta} = \frac{h}{x}[/tex] (5)
Cosecant
[tex]\csc \theta = \frac{1}{\sin \theta} = \frac{h}{y}[/tex] (6)
Where:
[tex]x[/tex] - Adjacent leg.
[tex]y[/tex] - Opposite leg.
[tex]h[/tex] - Hypotenuse.
The length of the hypotenuse is determined by the Pythagorean Theorem:
[tex]h = \sqrt{x^{2}+y^{2}}[/tex]
If [tex]y = AC[/tex] and [tex]x = BC[/tex], then the trigonometric ratios are presented below:
[tex]\sin \theta = \frac{AC}{\sqrt{AC^{2} + BC^{2}}}[/tex]
[tex]\cos \theta = \frac{BC}{\sqrt{AC^{2} + BC^{2}}}[/tex]
[tex]\cot \theta = \frac{BC}{AC}[/tex]
[tex]\sec \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{BC}[/tex]
[tex]\csc \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{AC}[/tex]
Related Questions
Help me please i need to hand this in
Answers
Hope this helps
A teacher asks her students to write down the number of hours studied, rounded to the nearest half hour. She compiles the results and develops the probability distribution below for a randomly selected student. What is the mean of the probability distribution?
Probability Distribution
Hours Studied: X
Probability: P(X)
0.5
0.07
1
0.2
1.5
0.46
2
0.2
2.5
0.07
Answers
Answer:1.50
Step-by-step explanation:None
Answer: the answer is d
Step-by-step explanation:
Oscar is buying soil for his plants. He needs to fill one pot with 8 cups of soil and another pot with 3 gallons of soil. If
the price of soil is $2.50 per quart, how much, in dollars, will he pay in all? You may use the conversions to help you
answer the question
1 cup = 8 fluid Ounces
1 pint = 2 cups
1 quart = 2 pints
1 gallon = 4 quarts
1 gallon = 3.875 liters
Enter your answer in the space provided
Answers
Answer:
$35
Step-by-step explanation:
8 cups /2 = 4 pints
4/2 = 2 quarts = 5 dollars for first pot
3*4 = 12 quarts, = 30 dollars for second pot
find the surface area of the shape.
Answers
Answer:
268 m²
Step-by-step explanation:
8x26=208
3x10x2=60
208+60=268
Hi guys, I really need help, I reckon this is easy for you but I'm low-key disabled and need help with this question so please help me thx. <3
Answers
Answer:
15, 8, 66%, 40
Step-by-step explanation:
Hi! ok so in ogive charts its really about finding the corresponding data points and sometimes it's a lot of estimation so these answers may not be exact but they'll be close.
In the image, you'll see a bunch of lines, basically what youre doing is finding the corresponding frequency of the dollars or vice versa.
question a)
50 dollars or less, so the area of 50 dollars and below that.
from the chart we can see that this lines up to around 15 people.
question b)
now this one is a little bit more challenging, but you can use the same process as you did for the first question. so we can see who spent 100 dollars or less. this value is around 42 (just from looking at the graph)
we know if you didn't spend 100 dollars or less, you must have spent more than that.
so take 50-42=8
around 8 people spent 100 dollars or more.
question c)
basically the same question as the first but more calculations are involved. from the graph we can see around 33 people spent 80 dollars or less. but the question is asking the percentage. so what percent of 50 (people) is 33.
33/50 = 0.66
around 66%
question d)
80th percentile means less than or equal to 80% of the frequencies/the data. so we first need to find what value that is in terms of frequency.
50 times 0.8 = 40
40 people
now just plot that on the graph (sorry i did it wrong in the image)
A small radio transmitter broadcasts in a 31 mile radius. If you drive along a straight line from a city 38 miles north of the transmitter to a second city 36 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter? Hint: assume that the transmitter is at the origin. Write the equations of the line and circle.
Answers
9514 1404 393
Answer:
63.7% or 33.35 miles
Step-by-step explanation:
The hint suggests that we find the points where the drive begins and ends picking up the transmitter. We suspect both of those points will have irrational coordinates, so finding the distance between them will involve dealing with squares and roots of irrational numbers. We want to see if there's an easier way.
The distance from the transmitter to the path being driven can be found using the "distance to a line" formula. First, we need the equation of the line in general form. In intercept form, it is ...
y/38 +x/36 = 1
19x +18y -684 = 0 . . . . . . multiply by LCM(36, 38) and subtract that amount
Then the distance from the origin to the line is ...
d = |19·0 +18·0 -684|/√(19² +18²) = 685/√685 ≈ 26.1243
The distance (x) along the line from the point where the transmitter is first picked up until the point of closest approach can be found from the Pythagorean theorem:
x² + (26.1243)² = 31²
x² = 31² -(684/√685)² = 190429/685
x ≈ 16.6733
The driving distance for which the transmitter is picked up is twice this, so is ...
2x = 2(16.6733) ≈ 33.3466 . . . miles
The total drive length is also given by the Pythagorean theorem:
drive length = √(36² +38²) = √2740 ≈ 52.3450 . . . miles
Then the fraction of the drive during which the signal is picked up is ...
fraction = (33.3466 mi)/(52.3450 mi) ≈ 0.6371 ≈ 63.7%
__
The signal is picked up for 33.35 miles, about 63.7% of the drive.
______
The intercept-form equation for a line is ...
x/(x-intercept) +y/(y-intercept) = 1
The distance from (x, y) to line ax+by+c=0 is given by ...
d = |ax+by+c|/√(a²+b²)
The Pythagorean theorem relates legs a, b and hypotenuse c of a right triangle this way:
c² = a² +b²
Jill bought 3 boxes of ice pops. Each box contains 4 orange ice pops and some cherry ice pops. The number of cherry ice pops in each box was the same. Jill bought 36 ice pops in all. What are the 2 steps of this equation and how many cherry ice pops are in each box?
Answers
Answer: 9 cherry ice pops
Step-by-step explanation:
if you bought 3 boxes and there is four orange one in each pack the that is
12 and 36 divided by 4 is 9 so there is 9 cherry ice pops
Hi plz help, if you can ill mark you 5 starz! :)
Answers
Answer:
b and 288
Step-by-step explanation:
ywwwwwwwwwwww
is 0.45 greater than 0.5
Answers
Answer:
0.5
hope this helps
have a good day :)
Step-by-step explanation:
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Bailey has been studying wait times at two restaurants in her hometown.
Which TWO statements BEST describe the relationship between the restaurant wait times?
A
If two sets of data have the same median, they will also have the same range.
B
The mode can not be used to compare this data because there are multiple modes for restaurant B.
C
There is less of a wait time for restaurant A because the range of the data is less than the range of the data for restaurant B.
D
When comparing two sets of data, the closer the means of the data are, the greater the data will visually overlap when graphed.
E
When there is a large difference between the means in two sets of data, there will also be a large difference in the medians of the data sets.
Answers
which table of values would you use to graph y = 3X^2?
Answers
Answer:
y because its y i really dont no
A triangle has side lengths of
[tex] \sqrt{125} [/tex]
[tex] \sqrt{5} [/tex]
[tex] \sqrt{20} [/tex]
What is the perimeter of the triangle?
[tex]4 \sqrt{5} [/tex]
[tex]6 \sqrt{5} [/tex]
[tex]8 \sqrt{5} [/tex]
none of the answers are correct
Answers
Answer:
3 is the right one
Step-by-step explanation:
Simple math you know
Find the volume of this rectangular prism. 3 in 3 in 8 in
Answers
Answer: 72
Step-by-step explanation: LxWXH
3x3x8=72
The perimeter of the figure below is 141.8ft. Find the length of the missing side
Answers
Answer:8.6
Step-by-step explanation:
The easiest way to do this is for you to subtract all the sides from the total perimeter since the perimeter is all of the sides added and your remainder is your answer
Hope this helps
Answer:
8.6 ft
Step-by-step explanation:
Subtract the sum of the known sides from the total in order to find the missing side length.
141.8 - (44.8 + 12.9 + 12.9 + 22.4 + 13.4 + 13.4 + 13.4) = ?
141.8 - (133.2) = ?
8.6 = ?
Find the sum of the first four terms of the geometric series 100 + 50 + 25 + ...
Answers
Answer:
Decimal:
100 + 50 + 25 + 12.5 + 6.25 + 3.125 + 1.5625
Fraction:
[tex]100 +50+25 + 12\frac{1}{2}+6\frac{1}{4}+3\frac{1}{8}+1\frac{9}{16}[/tex]
A car rental company charges $11 a day and 18 cents per mile to rent their cars. If the total charge for a 2-day rental was $61.60, how many miles were driven? Write and solve and equation.
Answers
Answer:
220 miles
Step-by-step explanation:
.18m + 11d = 61.60
d = 2
.18m + 22 = 61.60
Subtract 22 from both sides
.18m = 39.60
Divide both sides by .18
m = 220
Calculate the scale factor of ABC to DEF. Enter answer as a whole number or as a fraction in lowest terms, using the slash mark ( / ) for the fraction bar.
Answers
Answer:
3
Step-by-step explanation:
because 3x3= 9 and 4x3=12 and 5x3=15
write an equivalent expression for 3/5x + 2/5 + 3/5x
please i will give brainliest
Answers
Answer:
= 3/5(x) + 3/5(x) + 2/5
= 6/5(x) + 2/5
= 2/5 (3x+1)
Step-by-step explanation:
Answer: [tex]\frac{6}{5}x + \frac{2}{5}[/tex]
This is the same as writing (6/5)x + 2/5
===================================================
Explanation:
Ignore the fraction [tex]\frac{2}{5}[/tex] for now.
The other terms will combine together since they are like terms. We'll add those terms to get:
[tex]\frac{3}{5}x+\frac{3}{5}x\\\\\left(\frac{3}{5}+\frac{3}{5}\right)x\\\\\frac{3+3}{5}x\\\\\frac{6}{5}x\\\\[/tex]
Then we tack on the [tex]\frac{2}{5}[/tex] we ignored earlier to get the final answer of [tex]\frac{6}{5}x+\frac{2}{5}[/tex]
10
Select the correct answer from the drop-down menu.
The solution set for 6a2 - a -5 = 0 is
Reset
Next
Answers
Answer:
a = {-5/6 , 1}
Step-by-step explanation:
6a² - a -5 = 0
Factor
(6a + 5)(a - 1) = 0
Root 1
6a + 5 = 0
6a = -5
a = -5/6
Root 2
a - 1 = 0
a = 1
Solution set
a = {-5/6 , 1)
You have at most 8 hours to spend at a concert and at park. You want to spend at least 3 hours at the concert and more than 4 hours at the park.
Answers
The sum of two numbers is 80 and the difference is 20. What are the two
numbers?
Answers
Answer:
30 and 50
Step-by-step explanation:
its simple if you cant figure it out then drop out
Need help ASAP anybody got this??
Answers
Answer: uhm 6
Step-by-step explanation:
im not sure, but
1. y=9x
2. y=2x
The sum of 4 and x
4 + x
4 - x
4x
Answers
Answer:
16
Step-by-step explanation:
ezz
Wat is the Ans?
Got the question
Answers
Answer:
C
Step-by-step explanation:
C= 2* pi*r = 2* pi* 5 ≈ 31.4 cm
Find the number if 1/3 of it is 12?
Answers
Answer:
36
Step-by-step explanation:
If 1/3 of x is 12, we can make an equation.
x/3=12
So now we isolate x.
x=36
Answer:
36
Step-by-step explanation:
of means multiply and is means equals
1/3 * n = 12
Multiply each side by 3
3 * 1/3 n = 12 *3
n = 36
a farmer estimates that 6% of his plants will be eaten by rabbits. if he has 550 plants, how many will be eaten by rabbits?
Answers
Answer:
33 plants
Step-by-step explanation:
6 x 550 = 3300
3300/100 = 33
In a class of 6 there are 4 students who are secretly robots
Answers
Answer:
then 2 are human
Step-by-step explanation:
because 4 are robots
Answer:
The rest are normal students.
6-4= 2 so that's how many normal students there are.
Please add a little bit more detail to the question please :)
Seeking help to solve the problem shown in the image.
Answers
9514 1404 393
Answer:
1340
Step-by-step explanation:
The perimeter of a rectangle of length L and width W is ...
P = 2(L+W)
The perimeter of the rectangle outline of the figure is ...
P = 2(315 +300) = 2·615 = 1230
That outline is the sum of all of the line segments making up the figure except for two lengths of 55 units each. Adding those, we find the perimeter of the figure to be ...
P = 1230 +2(55) = 1230 +110 = 1340 . . . units
_____
Additional comment
It can be convenient to consider the total of horizontal segments and the total of vertical segments. We have shown in the attachment that, except for the 55-unit "indent", the horizontal and vertical lengths are equivalent to those of an ordinary rectangle. Thinking about the problem in this way makes it unnecessary to do the tedious arithmetic necessary to find each segment length. (Here, there is not enough information to do that anyway.)
Can someone help me please
Answers
The graph shows a linear function.
아이가
10!
8
6
4
2
-10-8-6-4
-3
24
10
-6
-104
Which table of values has a smaller rate of change than the function in the graph?
y
-6
X
-6
-7
y
3
4
5
6
OA.
Ос.
0
1
5
1
2
16
0
3
9
х
B.
E-6 -8
-4
03-5
2-4
81
- 2
0 2
3114
418
Answers
9514 1404 393
Answer:
table C
Step-by-step explanation:
The rates of change can be computed using the slope formula.
m = (y2 -y1)/(x2 -x1)
The points used and the resulting "rate of change" are shown in the attachment.
Table C shows a rate of change (1/3) that is less than that of the graph (1/2).
_____
I like to use a spreadsheet for repetitive calculations, especially ones involving negative numbers. This helps prevent errors (and tedium). The formula is entered only once.
The table of values which has a smaller rate of change than the function in the graph is C.
What is Slope?This is defined as the ratio of the vertical change to the horizontal change between any two distinct points on a line.
Slope formula.
m = (y2 -y1)/(x2 -x1)
For table C = 4 -3 / -3 - (-6)
= 1/3
Table C shows a rate of change of 1/3 which is less than that of the graph at 1/2 .
Read more about Slope here https://brainly.com/question/25722412