find the values of the six trigonometric functions for angle theta in standard position if a point with the coordinates (1, -8) lies on its terminal side
Answer:
cosФ = [tex]\frac{1}{\sqrt{65}}[/tex] , sinФ = [tex]-\frac{8}{\sqrt{65}}[/tex] , tanФ = -8, secФ = [tex]\sqrt{65}[/tex] , cscФ = [tex]-\frac{\sqrt{65}}{8}[/tex] , cotФ = [tex]-\frac{1}{8}[/tex]
Step-by-step explanation:
If a point (x, y) lies on the terminal side of angle Ф in standard position, then the six trigonometry functions are:
cosФ = [tex]\frac{x}{r}[/tex]sinФ = [tex]\frac{y}{r}[/tex]tanФ = [tex]\frac{y}{x}[/tex]secФ = [tex]\frac{r}{x}[/tex]cscФ = [tex]\frac{r}{y}[/tex]cotФ = [tex]\frac{x}{y}[/tex]Where r = [tex]\sqrt{x^{2}+y^{2} }[/tex] (the length of the terminal side from the origin to point (x, y)You should find the quadrant of (x, y) to adjust the sign of each function∵ Point (1, -8) lies on the terminal side of angle Ф in standard position
∵ x is positive and y is negative
→ That means the point lies on the 4th quadrant
∴ Angle Ф is on the 4th quadrant
∵ In the 4th quadrant cosФ and secФ only have positive values
∴ sinФ, secФ, tanФ, and cotФ have negative values
→ let us find r
∵ r = [tex]\sqrt{x^{2}+y^{2} }[/tex]
∵ x = 1 and y = -8
∴ r = [tex]\sqrt{x} \sqrt{(1)^{2}+(-8)^{2}}=\sqrt{1+64}=\sqrt{65}[/tex]
→ Use the rules above to find the six trigonometric functions of Ф
∵ cosФ = [tex]\frac{x}{r}[/tex]
∴ cosФ = [tex]\frac{1}{\sqrt{65}}[/tex]
∵ sinФ = [tex]\frac{y}{r}[/tex]
∴ sinФ = [tex]-\frac{8}{\sqrt{65}}[/tex]
∵ tanФ = [tex]\frac{y}{x}[/tex]
∴ tanФ = [tex]-\frac{8}{1}[/tex] = -8
∵ secФ = [tex]\frac{r}{x}[/tex]
∴ secФ = [tex]\frac{\sqrt{65}}{1}[/tex] = [tex]\sqrt{65}[/tex]
∵ cscФ = [tex]\frac{r}{y}[/tex]
∴ cscФ = [tex]-\frac{\sqrt{65}}{8}[/tex]
∵ cotФ = [tex]\frac{x}{y}[/tex]
∴ cotФ = [tex]-\frac{1}{8}[/tex]
Write an inequality representing the following phrase:
One-tenth of a number h is less than or equal to ten
Answer:
[tex]\frac{1}{10} h\leq 10[/tex]
Step-by-step explanation:
Basically, we are just translating the phrase into an algebraic expression.
Which of these is the triangle proportionality theorem? First person to answer CORRECTLY gets brainliest
Answer: A.
Step-by-step explanation: Brainliest plz
find the value of x
The answer is 150.
I need to show my work.
THANKSSSS
Answer:
x = 150
Step-by-step explanation:
We know a circle is 360°, so the angles must add up to 60°.
Step 1: Set up equation
x - 120 + x - 120 = 60
Step 2: Solve for x
Combine like terms: 2x - 240 = 60Add 240 on both sides: 2x = 300Divide both sides by 2: x = 150Step 3: Check
Plug in x to verify it is correct.
150 - 120 = 30°
150 - 120 = 30°
30° + 30° = 60°
60° + 300° = 360°
The quanities x and y are proportional Find the constant of proportionality (r) in the equation y= rx
CORRECT ANSWER = BRAINLEIST
Answer:
5
Step-by-step explanation:
7*5=35
12*5=60
20*5=100
HELP ME PLEASE IM ALMOST TO 100
Answer:
= 3/4
Step-by-step explanation:
Find 2 points on the graph
(2,3) and (6,6)
Using the slope formula
m = (y2-y1)/(x2-x1)
= ( 6-3)/(6-2)
= 3/4
So Can anyone help me with this
what is 4/6+2/3.?(these are fractions, you're just adding fractions)
Answer:
4/3
Step-by-step explanation:
Multiply 2 by 2, and get 4, then we multiply 3 by 2 and get 6.
Since our denominators match, we can add the numerators. 4 + 4 = 8. That gives us the sum, which is 8/6. Then you divide by 2. So 8/6 / 2 gives you 4/3.
Answer:
4/3 or 1 1/3
Step-by-step explanation:
1. 4/6 + 2/3
2. 4/6 + 4/6 You have to find the LCM (least common multiple) of the two denominators. In this case it would be 6. You have to multiply 3 by 2 to get 6. What you do to the bottom you also do to the top so you have to also multiply the numerator (2) by 2.
3. 4/3 or 1 1/3 Afterward, you just have to add straight across without changing the denominator and then if you need to simplify you simplify. Without simplifying, you would get 8/6, but, most teachers will mark it as wrong if you don't simplify. You can then change the improper fraction into a mixed number depending on what your teacher wants.
13
In the figure shown below, if line mis parallel to line n, then find the value of x. (This is a 2 part question.)
m
(2x-10)
(65 - x)
Part A
Write the equation to find the value of x. (DO NOT find x, just write the equation.)
(2x - 10) (65 - x)
Part B
What is the value of x?
Y
Answer:
2x-10 = 65-xStep-by-step explanation:
just add up both alternate internal angles as they are both equal
so, the equation is: 2x-10 = 65-x
Answer:
The right equation will be 2x - 10 = 65 - x (you were wrong lol)
Step-by-step explanation:
We have: 2x - 10 = 65 - x
=> 2x - 10 + x = 65
=> 3x = 65 + 10 = 75
=> x = 75/3 = 25
P/S: After some little chats with the others, this might be wrong :(
Caleb and Sergio stacked boxes on a shelf. Caleb lifted 14 boxes and Sergio lifted 12 boxes. The boxes that Sergio lifted each weighed 10 lb more than the boxes Caleb lifted.
Let c represent the weight of each box Caleb lifted.
Which expression represents the total number of pounds Sergio lifted?
120c
10(c−12)
12(c+10)
c + 10
Answer:
b
Step-by-step explanation:
Answer:
12 c+10
Step-by-step explanation:
becus
1. You are eating on a Tootsie Roll Lollipop that is in the shape of a sphere. It is giving up volume at a steady rate of 0.25 in3 /min. How fast will the radius be decreasing when the Tootsie Roll Pop is .75 inches across?
Answer:
Step-by-step explanation:
Since the Tootsie Roll lollipop is a sphere
volume of sphere= [tex]\frac{4}{3}piR^3[/tex] = -0.25 [tex]in^3/min[/tex]
the negative sign indicates that the volume is decreasing
upon differentiating
as the diameter given is =0.75 so radius will be = 0.375
[tex]dV/dt = 4piR^2*dR/dt[/tex]
so [tex]dR/dt = 0.25/4*3.14 *(0.375)^2[/tex]
So the radius is decreasing at the rate of dR/dt= 0.142in/min
Select all the conditions for which it is possible to construct a triangle.
Group of answer choices
A triangle with angle measures LaTeX: 60^\circ 60 ∘ , LaTeX: 80^\circ 80 ∘ , and LaTeX: 80^\circ 80 ∘
A triangle with side lengths 4 cm, 5 cm, and 6 cm
A triangle with side lengths 4 cm, 5 cm, and 15 cm
A triangle with side lengths 4 cm and 5 cm and a LaTeX: 50^\circ 50 ∘ angle
A triangle with angle measures LaTeX: 30^\circ 30 ∘ and LaTeX: 60^\circ 60 ∘ , and a 3 cm side length
Answer:
A triangle with side lengths 4 cm, 5 cm, and 6 cm
A triangle with side lengths 4 cm, 5 cm, and 15 cm
A triangle with side lengths 4 cm and 5 cm and a 50∘ angle
A triangle with angle measures 30 ∘ and 60 ∘ , and a 3 cm side length
Step-by-step explanation:
A triangle measuring 60 ∘, 80∘ and 80∘ is more than sum of angles of a triangle (180∘). This cannot be constructed as triangle because it is more than 180∘.
A triangle can be constructed, If the sum of any two sides is greater than third side,
Thus, a triangle with side lengths 4 cm, 5 cm, and 6 cm can be constructed because;
4 cm + 5cm > 6 cm
A triangle with side lengths 4 cm, 5 cm, and 15 cm can be constructed as well, because;
5 cm + 15 cm > 4 cm
A triangle with side lengths 4 cm and 5 cm and a 50 ∘ angle can be constructed ( two sides and an angle between them)
A triangle with angle measures 30 ∘ and 60 ∘ , and a 3 cm side length can be constructed ( two angles and a side between them)
If your gross annual income is $80,400 and your employer will match 50% of your retirement
contributions to your 401k up to your maximum contributions of 6% of your salary, what is
the maximum dollar amount that together you and your employer will contribute annually?
Answer:
Well, due to the 6% add on, you could go up to 85,400 within the first year, however I am not quite sure for the 401k. Have a good day!
Step-by-step explanation:
(4.3 x 10^-3)(2 x 10^-2) in standard form
Answer:
8.6•10^-5 or 0.000086
Quickkkk!!!!!!!! Help
Answer:
2143
Step-by-step explanation:
Write a positive or negative integer that represents the situation.
An elevator goes down 8 floors.
A TV show has 26 episodes. Due to the lack of time, you can onlywatch 5 of them. However, in order to get a gist of what the showis about, you do not want to watch any two consecutive episodes.How many selections of 5 episodes are there with no two consecutiveepisodes chosen? Assuming that the order of selection is irrelevant.(Hint:this is a Stars and Bars problem)
Answer:
Step-by-step explanation:
Recall that: The number of combination to select any k consecutive element from n consecutive term is given by the equation [tex]^{n-k+1}C_k[/tex]
[tex]= \begin {pmatrix} ^{n-k+1}_{k} \end {pmatrix}[/tex]
where:
n = 26
k = 5
[tex]^{n-k+1}C_k= \begin {pmatrix} ^{26-5+1}_{5} \end {pmatrix}[/tex]
[tex]^{n-k+1}C_k= \begin {pmatrix} ^{22}_{5} \end {pmatrix}[/tex]
[tex]^{n-k+1}C_k= \dfrac{22!}{5!(22-5)!}[/tex]
[tex]^{n-k+1}C_k= \dfrac{22!}{5!(17)!}[/tex]
[tex]\mathbf{^{n-k+1}C_k=26334}[/tex]
Therefore, there are 26334 selection of 5 episodes with no two consecutive episodes chosen
HELP! Will be giving branliest!!!!!!
A is the right anwer to your Question because of the Hours and weeks
One of the dog treats in Shelley’s shop is 8 inches long and 3.2 inches wide. She wants to make a miniature version that has proportional dimensions. If the miniature treat will be 3 inches long, how wide should it be?
Answer:
1.2in
Step-by-step explanation:
Answer:
(1) 1.2 inches
What are the coordinates of the point (2, −3) after a counterclockwise rotation of 90° about the origin?
Answer:
-2,-3
Step-by-step explanation:
Please answer these giving brainliest to the first right person. 20 points.
Answer:
31.x>2
32.x<-2
33.x<5
34.x>0
Step-by-step explanation:
if loga81=4, find value of a?
Answer:
[tex]\huge\boxed{a=4}[/tex]
Step-by-step explanation:
[tex]\log_xy=z\iff x^z=y\\\\\text{for}\ x\neq1\ \wedge\ x>0\ \wedge\ y>0\\==================\\\\\log_a81=4\iff a^4=81\\\\a^4=\underbrace{3\cdot3\cdot3\cdot3}_{=81}\\\\a^4=3^4\Rightarrow a=3[/tex]
what is Pi? explain.
Answer:
Pi is a irrational number
Step-by-step explanation:
Pi is an irrational number because it never ends it keeps going on and one.
Pi is also 3.141592654.............. never ends
v (t) = 32,000 (0.84)
Find the initial value of the car and the value after 11 years.
Round your answers to the nearest dollar as necessary
Answer:
c
Step-by-step explanation:
c because
If 24 divided by 4 is 6 what is the remainder?
The remainder from the given division is 0.
Given that, 24 divided by 4 is 6.
The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Here,
4|24|6
24
______
0
So, the remainder is 0.
Therefore, the remainder from the given division is 0.
To learn more about the division visit:
https://brainly.com/question/1575906.
#SPJ6
if there are 7 fish and 3 drown how many are left?
Answer:
7
Step-by-step explanation:
there are 7 left because fish can't drown
What is the answer tho
Answer:
to?
Step-by-step explanation:
• Number Sense Write an addition
sentence and a multiplication
sentence to solve this problem.
Jessie bought 4 packages of colorful
stones to put in the fish bowl. There
are 6 stones in each package. How
many stones did Jessie buy?
Answer:
addition sentence is 6+6+6+6=24
multiplication sentence is 6×4=24
Step-by-step explanation:
hope this helps
Nellie purchased 6.5 pounds of strawberries for $12.87. Calculate the cost of a single pound. (Round to the nearest tenth or cent when necessary)
Answer:
The answer is $1.98.
Step-by-step explanation:
The butterfly method shows how to do this. It is 12.87 over 6.5 equals x over 1. Cross-multiply to get 6.5x = 12.87. Divide both sides by 6.5 to get x = 1.98.
HELP ME ASAP!!! I WILL MARK BRAINLIEST!!
Answer:
Brand A ($2) is more expensive than Brand B ($1.50) (see below)
Step-by-step explanation:
First, you will have to find the slopes of both lines. Slope is y/x, which is the cost/meter or cost per meter.
Using the slope formula:
y2 — y1
m = ---------------
x2 — x1
Plug in any two points from both lines:
y2 — y1
m = --------------- = graph 1 (0, 0), (1,2)
x2 — x1
2 — 0
m = ---------------
1 — 0
2
m = --------------- = $2/m
1
_______graph 2_______
y2 — y1
m = --------------- = graph 2 (0, 0), (4, 6)
x2 — x1
6 — 0
m = ---------------
4 — 0
6 3
m = --------------- = ----------- = $3/2 m
4 2
Because you are unable to have an exact cost per meter of Brand B, you can use a ratio:
$3 = $x
2m = 1m
Cross multiply:
3 (1) = 2x
3 = 2x
x = (3 ÷ 2)
x = 1.5
So Brand B is $1.50 per meter while Brand A is $2.00 per meter. Brand B is cheaper.