in the accompanying diagram of the unit circle, the ordered pair _ represents the point where the terminal side of 0 intersection in the unit circle
Answers
The ordered pair of a unit circle is represented as:
[tex](x,y) \to (\sin(\theta),\cos(\theta))[/tex]
The point where the terminal side of [tex]\tehta[/tex][tex]\theta[/tex] intersect with the unit circle is: 240
The given parameter can be represented as:
[tex](x,y) \to (-\frac{\sqrt 3}{2},-\frac{1}{2})[/tex]
This means that:
[tex]\sin(\theta) = -\frac{\sqrt 3}{2}[/tex]
[tex]\cos(\theta) = -\frac{1}{2}[/tex]
Let the angle between the x-axis and the terminal side be [tex]\alpha[/tex]
So, we have:
[tex]\theta = 180 + \alpha[/tex]
Using [tex]\cos(\theta) = -\frac{1}{2}[/tex]
The equation becomes
[tex]\cos(180 + \alpha) = -\frac{1}{2}[/tex]
Apply cosine formula
[tex]\cos(180)*\cos(\alpha) - \sin(180)*\sin(\alpha) = -\frac{1}{2}[/tex]
[tex]-1*\cos(\alpha) - 0*\sin(\alpha) = -\frac{1}{2}[/tex]
[tex]-1*\cos(\alpha)= -\frac{1}{2}[/tex]
Divide both sides by -1
[tex]\cos(\alpha)= \frac{1}{2}[/tex]
Take arccos of both sides
[tex]\alpha= \cos^{-1}(\frac{1}{2})[/tex]
[tex]\alpha= \cos^{-1}(0.5)[/tex]
[tex]\alpha= 60[/tex]
Recall that:
[tex]\theta = 180 + \alpha[/tex]
[tex]\theta = 180 +60[/tex]
[tex]\theta = 240[/tex]
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Related Questions
Write the equation of the line in POINT SLOPE FORM that passes through the point
(1, -7) anu has slope of 4
Answers
Answer:
y+7=4(x-1)
Step-by-step explanation:
y-y₁=m(x-x₁)
m= 4
y- -7 = 4(x-1)
y+7=4(x-1)
En una tienda en la que todo está rebajado el 20% he comprado una casaca por la que he pagado 160 soles. ¿Cuál era el precio antes de la rebaja?
Answers
Answer:
200 soles
Step-by-step explanation:
De la pregunta anterior, se nos da un descuento del 20%.
Por lo tanto, la fórmula para resolver la pregunta anterior es:
Precio nuevo = Precio inicial - (Porcentaje de descuento × Precio inicial)
De la pregunta anterior,
Precio nuevo = 160 soles
Precio inicial = x
Porcentaje de descuento = 20% = 0.2
Por eso:
160 = x - (20% x x)
160 = x - 0.2x
160 = 0.8 veces
Dividir ambos lados por 0.8
160 / 0.8 = 0.8 / 0.8
x = 160 / 0.8
x = 200 soles
Por lo tanto, el Precio Inicial que es el precio antes de la venta es de 200 soles.
Suppose you have an isosceles triangle with a 90° angleIf the congruent sides each measure 9 feet, what is the length of the side across from the right angle?
Answers
Answer:
[tex]9\sqrt{2}[/tex] feet
Step-by-step explanation:
Consider the attached figure.
An isosceles triangle is a triangle in which two sides are equal.
[tex]AB=BC=9[/tex] feet
According to Pythagoras theorem,
square of hypotenuse is equal to sum of squares of other two sides.
[tex]AC^2=AB^2+BC^2\\AC^2=9^2+9^2\\AC^2=81+81\\AC^2=162\\AC=\sqrt{162}[/tex]
[tex]AC=9\sqrt{2}[/tex] feet
More angles? More Spain- without the S. Anyway here we go!
Answers
22) alternate interior
23) supplementary
What is the distance between (3,7) and (-3,-1) ?
Answers
Answer:
The answer is 2,889 mi Mark me brainliest if I'm right.
Step-by-step explanation:
NEED HELP FRERE BRAINLIST
Answers
Answer:
7.5
Step-by-step explanation:
[tex]a^2+b^2=c^2\\x^2+5^2=9^2\\x^2+25=81\\x^2=56\\\sqrt{x^2} =\sqrt{56} \\x=7.5[/tex]
how do i find a surface area of a triangle prism
Answers
Answer:
Triangular prisms have their own formula for finding surface area because they have two triangular faces opposite each other. The formula A=12bh is used to find the area of the top and bases triangular faces, where A = area, b = base, and h = height.
Hope it helps..
Have a great day
A membership price for the local pool went
from $80 to $60. What is the percent
change in membership cost?
Answers
7m
6m
3m
Find rev surface area of each prism
Answers
Answer:
126m
Step-by-step explanation:
7 x 6 x 3
Which ordered pair is this solution of the system graphed ?
Answers
You can see they intersect at (5,-3)
The solution is D
Answer:
what?
Step-by-step explanation:
What is the volume of a right circular cone with a radius of 3 units and a height of 6 units? pleas help asap
Answers
Answer:
18 units
Step-by-step explanation:
Answer:
18 units
Step-by-step explanation:
This question has two parts. First, answer Part A. Then, answer Part B. Part A Pete is making 8 identical fruit baskets as gifts. Each basket contains some apples and 12 oranges. Pete uses a total of 168 pieces of fruit to make the baskets. Which equation can be used to determine the number of apples, a, that are in each basket? Multiple choice question.
Answers
Answer:
a = 21 - 8
Step-by-step explanation:
to determine the number of apples in each basket, first determine the total number of fruits in each basket and subtract it from the number of oranges in each basket
number of fruits in each basket = 168 / 8 = 21
a = 21 - 8
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
Answers
Answer:
it should be C based on the p
Answer:
A.
Step-by-step explanation:
A is correct because the pizza(p) cost $6 not $2.50 and the Drinks(r) cost $2.50 not $6 so that already eliminates C and D.
And too chose between A and B is that did it need to be less than or equal too $50 (≤) .
or did it need too be more than or equal too 9p+2.5r (≥).
it needed to be less than or equal too $50 so it is ≤
Hope this helps!!
Darnell and Hector ride their bikes at constant speeds. Darnell leaves Hector’s house to bike home. He can bike the 8 miles in 32 minutes. Five minutes after Darnell leaves, Hector realizes that Darnell left his phone. Hector rides to catch up. He can ride to Darnell’s house in 24 minutes. Assuming they bike the same path, write the liner equation that represents darnells constant speed
Answers
9514 1404 393
Answer:
s = (8 mi)/(24 min/(60 min/h))
Step-by-step explanation:
Let s represent Darnell's constant speed. We know that speed, distance, and time have the relationship ...
speed = distance/time
Darnell's speed in miles per hour is ...
s = (8 mi)/(24 min/(60 min/h)) . . . . equation representing Darnell's speed
_____
This simplifies to ...
s = 20 mi/h
what dose 0.31 × 1.4 =
Answers
Solve the equation. Then check your solution.
Four-fifths + x = StartFraction 3 Over 7 EndFraction
a.
StartFraction 13 Over 35 EndFraction
c.
1 and StartFraction 8 Over 35 EndFraction
b.
Negative one-half
d.
Negative StartFraction 13 Over 35 EndFraction
Please select the best answer from the choices provided
A
B
C
D
Answers
Answer:
D -13/35 ( negative 13/35 )
Step-by-step explanation:
4/5 + x = 3/7
Convert to equivalent fractions with a common denominator:
28/35 + x = 15/35
Subtract 28/35 from both sides
x = - 13/35
Answer:here's the answer for this question
Step-by-step explanation:edge2023
Kendall spent 2/5 of the money she made babysitting on shirts. If she babysat for 6 hours and made 8 an hour. How much money did she have left after she bought the shirts.
Answers
Answer:
Step-by-step explanation:
Total hours work: 6 hours
Hourly wages: $8.00
Kendall total amount made for babysitting: 6 x $8 = $48.00
Total amount spent on shirts: $48 x 2/5 = $19.20
Amount of money Kendall had left after purchasing the shirt:
$48.00 - $19.20 = $28.80
find square root of 100
Answers
Answer:
10, -10
Step-by-step explanation:
Take the sqrt(100)
What number times itself = 100
10*10 = 100
-10*-10 = 100
sqrt(100) = +10 or -10
What is the value of the (2/3) exponet 3 times (3 + 6 x 4)
Answers
Answer: 24 | 8/9
Step-by-step explanation:
who is the father of politics
Answers
What value goes in the blank to give the unit rate? (Answers may contain decimals)
48 houses on 2 blocks = ________ houses per block
Answers
Answer:
24 houses per block!
Step-by-step explanation:
48÷2=24
PLEASE DON'T SPAM I NEED HELP:((
a) 1/6
b) 5/9
c) 6/5
d) 5/6
Answers
Answer:
5/6 chance of getting something greater than 4
Step-by-step explanation:
I need this done today whoever gets this correct gets brainliest!!! PLZZ HELPP MEE!!!
hurryy
Answers
Answer:
1) true
2) false
3) true
4)false
Step-by-step explanation:
It's a number cube with 1-6
w Circumference (definition)
Answers
Answer:
Definition: The enclosing boundary of a curved geometric figure, especially a circle.
Step-by-step explanation:
what is
[tex]35 \sqrt{9} \div 7 \sqrt{3} [/tex]
Answers
A cereal box has a length of 4 inches, a width of 5 inches,
and a height of 8 inches. What is the volume of the box?
Justify your answer
Answers
Answer:
160
Step-by-step explanation:
base x width x height = volume
4x5x8=160 in^3
That's all there is to volume of a box
Hope that helps :)
Answer:
160 yet it's supposa be in Cuboid e.g. 160cm3
Step-by-step explanation:
Volume=L×H×W
= 4×5×8
=160
A hostel has food for 600
students for 50 days. After 15 days, if 180 students leave
the hostel, how long will the food last?
Answers
Answer:
Answer is 35
Step-by-step explanation:
After 15 days, 600-180=420.
After 15 days, 600-180=420.Therefore, 600 : 50
After 15 days, 600-180=420.Therefore, 600 : 50 420 : X
Let X represent the number of days.
So now, X. × 50
X. × 50 ----. ----. Or Simply 50/ 600= 1/12
X. × 50 ----. ----. Or Simply 50/ 600= 1/12 420. 600.
No u cross multiply this fraction.
Which is, X × 12= 12X
X × 12= 12X 420 × 1 = 420
U have to let X stand alone.
12X = 420
12X = 420 ------. -------
12X = 420 ------. ------- 12. 12
So now u cancel out, 12 will cancel 12 so X will stand alone.
So now 12 will cancel 420 which means 12 will go into 420, 35times.
Therefore X = 35
Meaning the hostel will feed the rest of the students for 35days.
The solid below is made from 1 foot cubes. Find the total surface area of the solid. Be sure to include the correct unit in your answer.
Answers
Explanation is in the file
tinyurl.com/wpazsebu
Jill was solving a system using the elimination method.After she added the equations together,she got 5=7.What does this mean for the system? Pls help!
Answers
Answer:
It means the system does not have a solution
Step-by-step explanation:
Sofia drew a scale drawing of a theater. The stage, which is 48 feet long in real life, is 16
inches long in the drawing. What scale did Sofia use?
1 inch:
feet
Answers
First, you multiply 4 by 1. Then that's your answer, 4. I hope it helped!