The six trigonometric functions related to (x, y) = (20, 48): sin θ = 12/13, cos θ = 5/13, tan θ = 12/5, cot θ = 5/12, sec θ = 13/5, csc θ = 13/12.
How to determine the six trigonometric functions from coordinates in rectangular form
Given the coordinates in rectangular form, that is, (x, y), where each component belongs to an orthogonal axis of reference. By trigonometry we have six functions to be calculated:
[tex]\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}[/tex] (1)
[tex]\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex] (2)
[tex]\tan \theta = \frac{\sin \theta}{\cos \theta}[/tex] (3)
[tex]\cot \theta = \frac{1}{\tan \theta}[/tex] (4)
[tex]\sec \theta = \frac{1}{\cos \theta}[/tex] (5)
[tex]\csc \theta = \frac{1}{\sin \theta}[/tex] (6)
If we know that x = 20 and y = 48, then the six trigonometric functions are, respectively:
[tex]\sin \theta = \frac{48}{\sqrt{20^{2}+48^{2}}}[/tex]
[tex]\sin \theta = \frac{12}{13}[/tex]
[tex]\cos \theta = \frac{20}{\sqrt{20^{2}+48^{2}}}[/tex]
[tex]\cos \theta = \frac{5}{13}[/tex]
[tex]\tan \theta = \frac{12}{5}[/tex]
[tex]\cot \theta = \frac{5}{12}[/tex]
[tex]\sec \theta = \frac{13}{5}[/tex]
[tex]\csc \theta = \frac{13}{12}[/tex]
The six trigonometric functions related to (x, y) = (20, 48): sin θ = 12/13, cos θ = 5/13, tan θ = 12/5, cot θ = 5/12, sec θ = 13/5, csc θ = 13/12. [tex]\blacksquare[/tex]
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4. The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is: (a) 587 × 10^8 miles,
(b) 587 × 10^10 miles,
(c) 587 × 10^-10 miles,
(d) 587 × 10^12 miles,
(e) 587 × 10^-12 miles
5,870,000,000,000 miles.
to find:The distance light travels in 100 years.
solution:The distance of the light travels in 100 years is:
5,870,000,000,000 × 100 miles.
= 587,000,000,000,000 miles
= 587 × 10^12 miles.
answer= option d
[tex]1 \: year = 5870000000000 \: miles[/tex]
To find:The distance which light can travel in 100 years.
Solution:to find the distance which light can travel in 100 years, multiply the distance which light can travel in 1 year (5,870,000,000,000 miles) by 100.
[tex] = 5870000000000 \times 100[/tex]
[tex] = 587000000000000 \: miles[/tex]
[tex] = 587 \times {10}^{12} [/tex]
Hence, the correct answer is option D
Can some help meeeeeeeee?
Answer:
$46.54
Step-by-step explanation:
A=P(1+r/n)^nt
P=220
r=.0325
n=1
t=6
A=266.54
A=P+I
266.54=220+I
I=46.54
Pls Help i'm stuck Solve for m∠C
m∠C =
Answer:
92 Degrees.
Step-by-step explanation:
As this is a Quadliateral inscribed in a circle, you can use a trick that is always true for these types of problems. Opposite angles will always be the same, since 92Degrees is A and is opposite to C, this means C is also 92Degrees, these type of shapes are also known as cyclic quadrilaterals
How many ways can Caroline choose 2 courses of each type?
Answer:
Step-by-step explanation:
I need more explanation to answer
Find the surface area of the cone in terms of pi. 15cm 3cm
Answer:
SA = 54π cm^2
A
Step-by-step explanation:
[tex]{\pi}rs + {\pi} {r}^{2} [/tex]
radius = 3cm
slant height = 15 cm
follow the formula
Graph this parabola
Show all steps please!!!
In this case, the equation is in vertex form. To graph the parabola, we need to determine the y-intercept, x-intercept(s), and the vertex.
Vertex of Parabola:Vertex form: y = a(x + h)² - k
⇒ [y = 3(x + 2)² - 1] and [y = a(x - h)² - k] ⇒ Vertex: (h, k) ⇒ (-2, -1)X-intercept(s) of Parabola:Assume "y" as 0.
[tex]\implies 0 = 3(x + 2)^{2} - 1[/tex]
[tex]\implies 1 = 3(x + 2)^{2}[/tex]
Take square root both sides and simplify:
[tex]\implies\sqrt{1} = \sqrt{3(x + 2)^{2}}[/tex]
[tex]\implies1 = \sqrt{3 \times (x + 2) \times (x + 2)}[/tex]
[tex]\implies1 = (x + 2) \times \sqrt{3[/tex]
Divide √3 both sides:
[tex]\implies \±\huge\text{(}\dfrac{1 }{\sqrt{3}} \huge\text{)} = (x + 2)[/tex]
[tex]\implies \±\huge\text{(}\dfrac{\sqrt{1} }{\sqrt{3}} \huge\text{)} = (x + 2)[/tex]
Multiply √3 to the numerator and the denominator:
[tex]\implies \±\huge\text{(}\dfrac{\sqrt{1} \times \sqrt{3} }{\sqrt{3\times \sqrt{3}}} \huge\text{)} = (x + 2)[/tex]
[tex]\implies \±\huge\text{(}\dfrac{\sqrt{3} }{3}} \huge\text{)} = (x + 2)[/tex]
[tex]\implies \±\huge\text{(}\dfrac{\sqrt{3} }{3}} \huge\text{)} - 2 =x[/tex]
[tex]\implies x = \underline{-2.6...} \ \text{and} \ \underline{-1.4...} \ \ \ \ (\text{Nearest tenth})[/tex]
Y-intercept of Parabola:Assume "x" as 0.
⇒ y = 3(0 + 2)² - 1⇒ y = 3(2)² - 1⇒ y = 3(4) - 1⇒ y = 12 - 1⇒ y = 11y-intercept = 11 ⇒ (0, 11)
Determining the direction of the parabola:Since the first cooeficient is positive (+3), the direction of the parabola will be upwards.
Determining the axis of symmetry line:Axis of symmetry line: x-coordinate of vertex
Axis of symmetry line: x = -2
Plot the following on the graph:
y-intercept ---> 11 -----> (0, 11)x-intercept(s) -----> -1.4 and -2.6 -------> (-1.4, 0) and (-2.6, 0)Vertex -------> (-2, -1)Axis of symmetry ----> x = -2Refer to graph attached.
Answer:
VertexVertex form of a quadratic equation:
[tex]y=a(x-h)^2+k\quad \textsf{where }(h,k)\:\textsf{is the vertex}[/tex]
Given equation: [tex]y=3(x+2)^2-1[/tex]
Therefore, the vertex is (-2, -1)
x-intercepts (zeros)The x-intercepts are when [tex]y=0[/tex]:
[tex]\implies 3(x+2)^2-1=0[/tex]
[tex]\implies 3(x+2)^2=1[/tex]
[tex]\implies (x+2)^2=\dfrac13[/tex]
[tex]\implies x+2=\pm\sqrt{\dfrac13}[/tex]
[tex]\implies x+2=\pm\dfrac{\sqrt{3}}{3}[/tex]
[tex]\implies x=-2\pm\dfrac{\sqrt{3}}{3}[/tex]
[tex]\implies x=\dfrac{-6\pm\sqrt{3}}{3}[/tex]
Therefore, the x-intercepts are at -2.6 and -1.4 (nearest tenth)
y-interceptThe y-intercept is when [tex]x=0[/tex]:
[tex]\implies 3(0+2)^2-1=11[/tex]
So the y-intercept is at (0, 11)
Plot the graphAs the leading coefficient is positive, the parabola will open upwards.Plot the vertex at (-2, -1)Plot the x-intercepts (-2.6, 0) and (-1.4, 0)Plot the y-intercept (0, 11)The axis of symmetry is the x-value of the vertex. Therefore, the parabola is symmetrical about x = -2
**You don't need to plot the axis of symmetry - I have added it so that it is easier to draw the curve**
The side lengths of four triangles are listed below.
Determine whether each triangle is a right triangle.
Select all options that do create a right triangle.
a. Sides 4,5,6
b. Sides 10,15,20
c. Sides 5,12,13
d. Sides 8,15,17
Answer:
C and D
Step-by-step explanation:
Use Pythagorean theorem to test
a^2 + b^2 = c^2 ? a and b are the shorter two sides c = longest side
Doing this for each data set shows C and D ARE rt triangles
What is the equation of the line that passes through the point (-2, 1) and has a
slope of 5/2?
Answer:
is it (3,3)
Step-by-step explanation:
(x,y)=(-2+5,1+2)
(x,y)=(3,3)
The mother gave the two sons the same amount of money. When the older son spent $ 275 and the younger $ 250, the younger had 3 times more money than the older. How much money did the mother give to each son? solution: 292
Answer:
Each son received from their mother $287.50
Step-by-step explanation:
3(x - 275) = x - 250
2x = 825 - 250
x = 287.50
$287.50 - $275 = $12.50
Check the answer:
After spending the older son has $12.50
$287.50 - $250 = $37.50
After spending the younger son has $37.50
$37.50 ÷ $12.50 = 3 times
On her paper route, Carla rides her bicycle 51.8 miles during a 14-day period. She rides th
same distance each day. How many miles does she ride each day on her paper route?
Answer:
She rides 3.7 Miles each day
Step-by-step explanation:
51.8 / 14 = 3.7
518 / 14 = 37 but you put a point inbetween 3 and 7 because the 8 in the original answer is in the tenths.
The graph of linear function g passes through the points (-7, -4) and (7, 6)
Answer:
C. The slope is 5/7, and the y-intercept is 1.Step-by-step explanation:
You must solve the slope-intercept form with the graph of the linear function g passing through the points.
Use the slope-intercept form.
[tex]\underline{\text{SLOPE-INTERCEPT FORM:}}[/tex]
[tex]\Longrightarrow: \sf{y=mx+b}[/tex]
M= slopeB= y-intercept.Use the slope formula.
[tex]\underline{\text{SLOPE:}}[/tex]
[tex]\Longrightarrow \sf{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]
(-7,-4) and (7,6)
y2=6y1=(-4)x2=7x1=(-7)[tex]\sf{\dfrac{6-\left(-4\right)}{7-\left(-7\right)}}[/tex]
Solve.
[tex]\sf{\dfrac{6-\left(-4\right)}{7-\left(-7\right)}=\sf{\dfrac{10}{14}=\dfrac{10\div2}{14\div2}=\dfrac{5}{7} }}[/tex]
Therefore, the slope is 5/7 and y-intercept is 1.The correct answer is C. "The slope is 5/7, and the y-intercept is 1."I hope this helps. Let me know if you have any questions.
Which of the following triangles have three sides of different length?
Mr. Richardson is driving to a town 85 miles away. He drives 35 miles per hour for 2 hours before stopping for lunch. He drives 6 more miles and stops for gas. Which expression shows how many miles Mr. Richardson has left to drive?
85 - (35 x 2) - 6
85 - 35 - 2 - 6
(85 - 35) x 2 - 6
85 - 35 + 2 - 6
Answer:
(a) 85 - (35 x 2) - 6
Step-by-step explanation:
The miles Mr. Richardson has left to drive will be the difference between the distance to his goal and the miles he has alread driven. The relation between distance, speed, and time can be used to find the miles he drove before lunch.
__
before lunchdistance = speed × time
miles before lunch = (35 mi/h) × (2 h) = (35 × 2) mi
total drivenThe total miles driven before stopping for gas will be ...
miles before stopping for gas = (miles before lunch) + (6 more miles)
= 35 ×2 +6 . . . miles
miles remainingThen the remaining miles are ...
remaining = trip miles - miles driven
= 85 -(35 ×2 +6)
= 85 - (35 ×2) -6 . . . . . miles left to drive
1
N
3
4.
5
6
7
Find the area of the figure. (Sides meet at right angles.)
5 cm
3 cm
B cm
5 cm
5 cm
4 cm
4 cm
Answer:
6000cm
Step-by-step explanation:
multiply all figures given
Find the value of sin C rounded to the nearest hundredth, if necessary.
20
E
11
D
Help PLEASE
Answer:
[tex]0.55[/tex]
Step-by-step explanation:
[tex]\displaystyle \sin C=\frac{opposite}{hypotenuse}=\frac{11}{20}=0.55[/tex]
What steps are used to find the mean of a data set? Use the following data set as an example: 5, 4, 2, 6, 4, 3
Answer:
The mean would be 4
Step-by-step explanation:
Steps to find the mean.
1. Least to greatest.
2,3,4,4,5,6
2. Add all the numbers.
2+3+4+5+5,6
=24
3. Divided by how many numbers you have.
24÷6
=4
Hope this helps! Mark me brainlest if you want, have a great day!! :))
Answer: It would be 4
Step-by-step explanation: Hope that helps!
So report cards are due tomorrow please help
Answer:
11-1 equals 10
Step-by-step explanation:
The tallest of a collection of wooden dolls stands 1 meter tall, and each successive doll is
half as tall as the one before it. If there are 8 dolls in the collection, which is closest to
the combined height of the dolls?
O A. 1.5 meters
O B. 2 meters
O C. 3.1 meters
O D.
4 meters
The combined height of the dolls when the tallest of a collection of wooden dolls stands 1 meter tall, and each successive doll is half as tall as the one before it is 2 meters.
What is geometric sequence?Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.
It can be given as,
[tex]S=\dfrac{a(1-r^n)}{1-r}[/tex]
Here, [tex]a_1[/tex] is the first term of the sequence, n is the number of terms, and r is the common ratio.
The tallest of a collection of wooden dolls stands 1 meter tall, and each successive doll is half as tall as the one before it.
The second doll is half of the first doll. Thus, the height of the second doll is,
[tex]a_2=\dfrac{1}{2}\\a_2=0.5\rm\;m[/tex]
Similarly, height of third doll,
[tex]a_3=\dfrac{0.5}{2}\\a_3=0.25\rm\;m[/tex]
Here, we see a pattern or sequence in the height of doll,
1,0.5,0.25......
For this series, the value of first term [tex]a_1[/tex] is 1, the number of dolls n is 8 and common ratio r is 0.5. Put the value in the above formula,
[tex]S=\dfrac{1(1-0.5^8)}{1-0.5}\\S=1.992\\S\approx 2\rm\; meters[/tex]
Thus, the combined height of the dolls when the tallest of a collection of wooden dolls stands 1 meter tall, and each successive doll is half as tall as the one before it is 2 meters.
Learn more about the geometric sequence here;
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On a grid, moving from 0,0 to 4,4 makes a line at a 90-degree angle.
true or false
The given statement is false statment because the line drawn has an inclination of 45°.
Given that,
On a grid, moving from 0,0 to 4,4 makes a line at a 90-degree angle. whether the statement is true or false is to be justified.
A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.
Here,
According to the question,
Moving from 0,0 to 4,4
Calculating the slope,
m = 4 - 0 / 4 - 0
m = 1
m = tanФ = 1
tanФ = 1
tanФ = tan 45°
Ф = 45°
Thus, the given statement is a false statment because the line drawn has an inclination of 45°.
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Which quadrant will (30,-45) fall into?
Answer:
Quadrant 4
Step-by-step explanation:
The x value is positive so it is either in 1 or 4
The y value is negative so it is either 3 or 4
To meet both conditions, it must be 4
help please???????? help lol.
Answer:
[tex]8 \frac{1}{25} [/tex]
Step-by-step explanation:
[tex]4 \frac{3}{5} + 3 \frac{11}{25} \\ (4 + 3) + ( \frac{3}{5} + \frac{11}{25} ) \\ 7 + \frac{26}{25 } \\ 7 + 1 \times \frac{1}{25} \\ 8 \frac{1}{25} [/tex]
[tex]4 \frac{3}{5} + 3 \frac{11}{25} [/tex]
to find:the simplest form.
solution:[tex] \frac{23}{5} + \frac{86}{25} [/tex]
[tex] = \frac{(23 \times 25) + (86 \times 5)}{5 \times 25} [/tex]
[tex] = \frac{575 + 430}{125} [/tex]
[tex] = \frac{1005}{125} [/tex]
[tex] = 8 \frac{1}{25} [/tex]
The quotient of 36 and 3 is j.
Solve for j.
Group of answer choices
j=108
j=16
j=12
j=112
Answer:
j=12
Step-by-step explanation:
Use the digits 1-9 at lost one time each to make the equation true and give the solution
Answer:
[tex]2-3x=6x-7\\x=1[/tex]
(There are a lot more combinations tho. Read more!)
Step-by-step explanation:
The first thing to notice is that the answer has to be a whole number and that there are only 5 spaces.
Another thing to notice is that one of the x's is negative.
So the easiest thing is to set [tex]x=1[/tex].
The we can work backwards. There are multiple solutions that we can use. But any combination that adds to the same number will work.
Such as:
[tex]2-3x=6x-7\\x=1[/tex]
or
[tex]2-5x=3x-6\\x=1[/tex]
And so on.
Please help!! Will mark brainlyest.
Answer:
4 units left
Step-by-step explanation:
if u look at point C and count the amount of lines it takes to get to its next spot, it us 4 units left
u can tell which shape is the original because it does not have little 1's next to its letters
The following figures show the first two steps of a proof of the pythagorean theorem. which of the following statements about this proof is false?
Answer: C
Step-by-step explanation:
The area of the larger square is a^2 and the area of the smaller square is b^2, so the area is a^2 + b^2, not (a+b)^2.
Find the solutions to 6x2 - 54 x = 0
Answer:
x = 2/9 or 0.2
Step-by-step explanation:
6 x 2 - 54x = 0
(6x2) = 12
12 - 54x = 0
Rearange the terms
-54x + 12 = 0
subtract 12 from both sides
-54x = -12
Divide both sides by the same factor
-54x/54 = -12/-54
then simplify
x=2/9 or 0.2
WHAT IS THE FORMULA FOR SEMICIRCLE AREA
Answer:
The formula for semicircle area is [tex]\frac{1}{2} \pi r^2[/tex]
Very similar to the formula for finding area of a circle, but since a semicircle is half of a circle, the formula will be revolving around halves.
Hi guys can you answer 5 to 9 please thx
Answer:
5. 2612.5 ≈ $2613
6. 848.4 ≈ $849
of 1. The book is on the
Answer: I write more than one choice . The book is on the table , desk , bed , chair or shelf.
Step-by-step explanation: hope it helps
The Value of x in A is _____, and value y in B is _____.