The angles, 60°, [tex]\displaystyle \frac{\pi}{4}[/tex] and [tex]\displaystyle \frac{\pi}{6}[/tex] are special angles that have known trigonometric ratio values.
First part;
The sine and cosine gives the coordinates of the tip of the radius of a unit circle as it rotates P(cos(θ), sin(θ))Second part;
With the knowledge of the sine and cosine of 60°, we have; sin(60°) = sin(120°), sin(240°) = -sin(60°), sin(300°) = -sin(60°)cos(120°) = -cos(60°), cos(240°) = -cos(60°), cos(300°) = cos(60°)Third part;
[tex]\displaystyle \frac{\pi}{4}[/tex] can be used to find the sine and cosine of [tex]\displaystyle \frac{3 \cdot \pi}{4}[/tex], [tex]\displaystyle \frac{5 \cdot \pi}{4}[/tex], and [tex]\displaystyle \frac{7 \cdot \pi}{4}[/tex] [tex]\displaystyle \frac{\pi}{6}[/tex], can be used to find the sine and cosine of [tex]\displaystyle \frac{5 \cdot \pi}{6}[/tex], [tex]\displaystyle \frac{7 \cdot \pi}{6}[/tex], and [tex]\displaystyle \frac{11 \cdot \pi}{6}[/tex]Reasons:
First Part;
Considering a unit circle with the center at the origin of the graph, we have;
The sine of the angle, θ, rotated by the radius is the vertical distance of a point P on the circle which is the location of the radius, from the horizontal axis.
The cosine of the angle, θ, is the horizontal distance of P from the vertical axis, such that we have;
The coordinates of point P = (cos(θ), sin(θ))
In the four quadrant, we have;
First Quadrant; All trigonometric ratios are positive
Second Quadrant; sine is positive
Third Quadrant; Tan is positive
Fourth Quadrant; Cosine is positive
Second part;
We have; At 120°, the point P is the same elevation from the horizontal axis, therefore;
sin(60°) = sin(120°) = 0.5·√3
However, the x-coordinate of the point P is in the negative direction, therefore, we get;
cos(120°) = -cos(60°) = -0.5
Similarly from the quadrant relationship, we have;
240° is in the third quadrant, and it is 60° below the negative horizontal line, therefore;
sin(240°) = -sin(60°) = -0.5·√3
cos(240°) = -cos(60°) = -0.5
300° is in the fourth quadrant, and it is 60° below the positive x-axis, therefore;
sin(300°) is negative and cos(300°) is positive
Which gives;
sin(300°) = -sin(60°) = -0.5·√3
cos(300°) = cos(60°) = 0.5
Third part;
[tex]\displaystyle \frac{\pi}{4} =45^{\circ}[/tex]
[tex]\displaystyle \frac{\pi}{6} =30^{\circ}[/tex]
The sine and cosine of 45° can be used to find the sine and cosine of (180° + 45°) = 225°, (360° - 45°) = 315°
Also, due to the mid location of the angle 45° on the quadrant, we have;
Another angles is the sines and cosine of (90° + 45°) = 135°
Therefore, [tex]\displaystyle \frac{\pi}{4}[/tex], can be used to find the sine and cosine of 135°, 225°, and 315°
[tex]\displaystyle 135^{\circ} = \mathbf{\frac{3 \cdot \pi}{4}}[/tex], [tex]\displaystyle 225^{\circ} = \frac{5 \cdot \pi}{4}[/tex], [tex]\displaystyle 315^{\circ} = \frac{7 \cdot \pi}{4}[/tex]
Therefore,
[tex]\displaystyle \frac{\pi}{4}[/tex] can be used to find the sine and cosine of [tex]\displaystyle \mathbf{\frac{3 \cdot \pi}{4}}[/tex], [tex]\displaystyle \mathbf{\frac{5 \cdot \pi}{4}}[/tex], and [tex]\displaystyle \mathbf{ \frac{7 \cdot \pi}{4}}[/tex]
Similarly, the sine and cosine of, [tex]\displaystyle \frac{\pi}{6}[/tex] = 30° can be used to find the sine and cosine of 150°, 210°, and 330°.
[tex]\displaystyle 150^{\circ} = \frac{5 \cdot \pi}{6}[/tex], [tex]\displaystyle 210^{\circ} = \frac{7 \cdot \pi}{6}[/tex], and [tex]\displaystyle 330^{\circ} = \frac{11 \cdot \pi}{6}[/tex]
[tex]\displaystyle \frac{\pi}{6}[/tex], can be used to find the sine and cosine of [tex]\displaystyle \mathbf{ \frac{5 \cdot \pi}{6}}[/tex], [tex]\displaystyle \mathbf{ \frac{7 \cdot \pi}{6}}[/tex], and [tex]\displaystyle \mathbf{\frac{11 \cdot \pi}{6}}[/tex]
Learn more about the sine and cosine of angles here:
https://brainly.com/question/4372174
Answer:
Step-by-step explanation:
The cosine value of an angle is the x coordinate of the point the angle corresponds to on the unit circle, and the sine value of an angle is the y coordinate of that point. 120, 240, and 300 all form 60 degree reference angles which in turn forms 30-60-90 triangles which help to find the sine and cosine of these corresponding angles. Pi/4 radians converts to 45 degrees which forms a 45-45-90 special triangle on the unit circle which has its own known trigonometric ratio. Pi/6 radians converts to 30 degrees which forms a 30-60-90 triangle on the unit circle which also has a known trigonometric ratio. These ratios help find the sine and cosine of the angles on the unit circle which corresponds to a point on the coordinate plane.
Rachel finished 3/4of the race in 6 hours. How long was the entire race?
Answer:
it will take a total of 8 hours to finish the race
Step-by-step explanation:
6h÷3/4=8
The circle passes through the point (-1.5, 2.5). What is its radius?
Choose 1 answer
2.5
V1.5
1.5
/2.5
What is the value of x in this equation? Enter your answer in the box.
(2.4 x 10^3) x (3 x 10^x) = 7.2 x 10^9
Answer:
6
Step-by-step explanation:
(2.4×10³)×(3×10^x)=7.2×10^9
(3x10^x)=(7.2×10^9)/(2.4×10^3)
3×10^x=3×10^6
10^x=10^6
*when bases are same ,powers are equated*
thus x=6
Hey help pls pls pls pls pls
Answer:
coefficient of xwrite the equation in slope-intercept form35Step-by-step explanation:
The value -105 is the coefficient of x.
The slope is most easily read from the equation when it is in slope-intercept form. In that form, the slope is the coefficient of x. You could say Kim forgot to write the equation in slope-intercept form.
When the equation is written in that form, it becomes ...
165 -105x +3y = 0
165 -105x = -3y . . . . subtract 3y
-55 +35x = y . . . . . . divide by -3
y = 35x -55 . . . . . . in slope-intercept form
The correct slope is 35.
jackie is saving money for a coat that costs $121 if she already has $61 and saves $15 each week in how many weeks can she buy the coat make a function table
Answer:
4 weeks
Step-by-step explanation:
Total cost of coat = $121
Money saved = $ 61
Will save $15 per week
So let x = number of week = $15x
Money saved + will save = Total cost of the coat
$61 + $15x = $121
-$61 = - $61
$15x = $60
x = $60 ÷ 15
x = 4
Use the equation 4.9x-1.9=27.5
What two properties of equality do you need to use to solve the equation?
The two properties of equality that is needed to solve for the equation are addition property of equality and division property of equality.
The price of a notebook in 2012 is $2000. In 2013, its value decreased by 30%. In 2014, its value decreased by 30% of its value in 2013. Find the value of the notebook at the end of 2013
Answer:
The value of the notebook at the end of 2013 is $980
Step-by-step explanation:
First, find 30% of 2,000. To do so you need to convert 30% into a decimal by dividing it by 100.
30% ⇒ 0.30
Now multiply 0.30 by 2,000 to find 30% of 2,000.
2,000 × 0.30 = 600
Subtract 600 from 2,000 to find the price of the notebook in 2013.
2,000 - 600 = 1,400
Now find 30% of 1,400 using the same process.
1,400 × 0.30 = 420
Subtract 420 from 1,400 to find the price of the notebook in 2014.
1,400 - 420 = 980
(-9z + 8) + (-3z - 6)
Answer:
-12z + 2
Step-by-step explanation:
yeah-ya........ right???
Define Rational number? And give some examples..
Answer:
Any number that can be written as a fraction with integers is called a rational number . For example, 17 and −34 are rational numbers. (Note that there is more than one way to write the same rational number as a ratio of integers. For example, 17 and 214 represent the same rational number.)
Andrea runs a fruit store. She started Sunday with 20 cherries in stock. During
the day, she sold 17 cherries and got a shipment of fresh cherries. The
shipment contained 4 times as many cherries as she started the day with.
How many cherries does Andrea have in stock at the end of the day?
Answer:
Andrea has 83 cherries in stock at the end of the day.
Step-by-step explanation:
starts with 20 cherries
sold 17 cherries
3 cherries remain
get 4 times as many she starts with 20×4= 80
80 + the 3 that remained
Find the diameter of a circle whose Circumfrence is 66 m
Answer:
21.00845
Step-by-step explanation:
πD = 66m
D = 66x 7/22
D = 21m is your answer brainlist me plz
PLEASE HELP ASAP I NEED ANSWER IN LESS THAN 9 HOURS
Answer:
I dont really know if this is right, but for 5, y=5. I don't know what 6 is. Sorry.
Identify the constant of proportionality from the graph.
Please help I’ll give brainlist just please help and please no links or spamming just please hurry and give me the answer thank you!!!
Answer:
y=3x
Step-by-step explanation:
you have to figure out what mutiply by your x give you y
2/1
3/6
when you divide you get 2
Solve the following:
2x - 7 = x + 3
4 3
Answer:
x = 10
Step-by-step explanation:
2x - 7 = x + 3
=> 2x - 7 = x + 3
=> x = 10
Therefore, x = 10.
Hoped this helped.
Answer: x=350
Step-by-step explanation:
Slow and steady wins the race. The leatherback sea turtle is the fastest known reptile, with a maximum speed of 21.92 21.9221, point, 92 miles per hour ( mph ) (mph)left parenthesis, start text, m, p, h, end text, right parenthesis. Which of the following equations, where d dd is distance in miles and t tt is time in hours, represents a speed that is less than that of the leatherback sea turtle?
Answer:
ang hirap naman plss answeer
Hurry !!!A typical barrel of bot-oil contains 70 liters of oil. If a hole in the barrel is causing a constant 6 liters an hour leak, use a function to show the amount of oil in the barrel over time.
Answer:
y = -6x + 70
Step-by-step explanation:
Since the amount of oil in the tank decreases constantly, we need to create a linear function. Using the base form, y = mx + b, we can replace -6 for m because volume decreases by 6 (or increases by -6) each hour, and +70 for b because we start off with 70 liters of oil. So we get y = -6x + 70, with x representing the number of hours, and y representing the volume of oil remaining.
Triangle DCB is congruent to triangle IGH what is an less than H
Answer:
no cuh
Step-by-step explanation:
What is the constant of this polynomial? 3x9 + 4x + 129
Answer:
129
Step-by-step explanation:
When referring to the constant in a polynomial, we're generally referring to the term that has no variables in it. Here, that term is 129.
The constant is 129.
Which inequality represents this sentence?
A number is at least 65
On < 65
On > 65
On > 65
On < 65
Answer:
n ≥ 65Step-by-step explanation:
A number is at least 65. It means the number n can be 65 or greater.
Its translation is:
n ≥ 65The answer options don't have this included.
Let the number be n
At least 65 means the number is equal to 65 or greater than 65.Hence here we use greater than equal to sign.Inequality:-
[tex]\\ \sf{:}\Rrightarrow n\geqslant 65[/tex]
A company is shipping toys
to stores in boxes. Each
box will hold 16 toys.
How many boxes will be
needed to ship 2,944 toys?
Answer:
184 boxes
Step-by-step explanation:
Hope it helps:)
how do you write the equation of the line that passes through the points (-9,4) and (7,-2)
Answer:
y = -3/8x+5/8.
Step-by-step explanation:
First, we'll find the slope. This is (y_2-y_1)/(x_2-x_1). So, we do -2 - 4 / 7 --9. This goes to -6/16. Simplifying gets us -3/8. Now, we have y= -3/8x + b. We can solve for b by plugging in points. Using the first point, it goes to 4 = 27/8+b, we can solve for b now, getting us 5/8. So, the complete equation is y = -3/8x+5/8.
Answer:
y = (-3/8)x + 5/8
Step-by-step explanation:
First we need to find the slope of the line connecting these two points. Slope is represented by m and is equal to rise/run.
Going from the first point to the second, we see x increasing by 16 (this is the run) and y decreasing by 6 (this is the rise). Thus, the slope of this line is
m = rise/run= -6/16, or -3/8.
Adapt the slope-intercept formula y = mx + b to this situation. From the point (-9, 4) we get x = -9 and y = 4, and m = -3/8. Then we have:
4 = (-3/8)(-9) + b, from which we get the y-intercept, b:
4 = 27/8 + b, or 32 = 27 + 8b, or 8b = 5, so that b = 5/8.
The equation describing this situation is y = (-3/8)x + 5/8.
Determine whether the data in the table can be modeled by a linear equation. Explain.
If possible, write a linear equation that represents y as a function of x
Answer:
yes, because they're varying in a constante rate
y = -1/2x +3.5
CAN SOMEBODY PLEASE HELP ME
Answer:
x and y are both equal to 57.5°
Step-by-step explanation:
180° - 65° = 115°
115 ÷ 2 = 57.5
helppppppppppppppppppppppppppp
Answer:
-1/2
Step-by-step explanation:
It is negative because of the direction the line.
It is one half because it rises one and runs two.
I hope this helps!
Answer:
The slope is -1/2
The slope intercept is 2
The form is y = 2 - 1/2x
HELP PLEASE
I NEED TO CHECK OFF THE TWO FUNCTIONS USED TO CREATE THE GRAPH BELOW
Leon has to drive 36 miles to work. If he can average a speed of 48 miles per hour, about how long does it take him to get to work each day? (Hint: Use the formula d = rt.)
1. a quarter of an hour
2. three-fourths of an hour
3. half an hour
4. more than an hour
Answer:
i think the answer is 45 mins sorry if im wrong
i cant decide if its b or d please help for brainlist !!!!!!!!!!!!!
This is right answer because option d only shows that y are multiples in sequence but this answer shows the correct sequence
A is correct! Our base number is 9 since it's at x = 0. The number gets smaller as x increases, so it will be 1/3 instead of 3.
Hope this helps :)
the production of wheat increases from 25 tons to 30 tons the percantage increase in prodution of wheat is
Answer:
20%
Step-by-step explanation:
The percentage change is the difference divided by the original amount, expressed as a percentage.
(30 -25)/25 × 100% = 20%
Production increased by 20%.
You have to multiply 7 by 19. Which equation uses the Distributive Property to take this problem apan
A. 7(10 + 9) = 70 + 16
CB B. 7(10 + 9) = 70 + 9
c. 7(10 + 9) = 70 +63
D. 7(10 + 9) = 17 +63
18x-3y=9 Y=6x-3 what is the answer
Answer:
NP (Not possible)
Step-by-step explanation:
When you find 'X', by inserting '6x-3' into the 'Y', you get:
18x - 3(6x-3) = 9
distribute:
18x -18x + 9 = 9
Subtract 9 from 9 = 0
Add like numbers (the x's), and it equals 0
0=0
You can't find x, rendering the equation 'NP'
Hopefully this answer is right and an option :)