Angle (theta) is in standard position. If (8,-15) is on the terminal ray of angle (theta), find the values of the trigonometric functions.
sin(theta)=
cos(theta)=
tan(theta)=
csc(theta)=
sec(theta)=
col(theta)=
What are the answers and how?
Answers
Answer:
[tex]\sin \theta =\frac{-15}{17}\\cos \theta =\frac{8}{17}\\\tan \theta =\frac{-15}{8}\\\csc \theta =\frac{-17}{15}\\\sec \theta =\frac{17}{8}\\\cot \theta =\frac{-8}{15}[/tex]
Step-by-step explanation:
Given: (8,-15) is on the terminal ray of angle
To find: All the trigonometric ratios
Solution:
Trigonometry is a branch of mathematics that explain relationship between the sides and angles of triangles.
If (x, y) lies on the terminal side of θ then [tex]r=\sqrt{x^2+y^2}[/tex]
[tex]r=\sqrt{(8)^2+(-15)^2}=\sqrt{64+225}=\sqrt{289}=17[/tex] units
[tex]\sin \theta =\frac{y}{r}=\frac{-15}{17}\\cos \theta =\frac{x}{r}=\frac{8}{17}\\\tan \theta =\frac{y}{x}=\frac{-15}{8}\\\csc \theta =\frac{1}{\sin \theta }=\frac{-17}{15}\\\sec \theta =\frac{1}{cos \theta}=\frac{17}{8}\\\cot \theta =\frac{1}{\tan \theta}=\frac{-8}{15}[/tex]
Related Questions
what is the value of x (12x+2)
Answers
Answer:
12x^2 +2x
Step-by-step explanation:
x* (12x+2)
Distribute
12x*x +2*x
12x^2 +2x
Find the area of the parallelogram. *
Captionless Image
28.12 sq cm
3.9 sq cm
11.3 sq cm
56.24 sq cm
None of the above
Answers
Answer:
28.12 cm^2
Step-by-step explanation:
I don't know what "length" and "bottom" mean as dimensions in a parallelogram, but if they are a side length and an altitude drawn to that side, then the area is 7.6 cm * 3.7 cm = 28.12 cm^2.
Factor each trinomial
y2 +13y+40
a
(y+8)(y+5)
(y+20)(y+2)
(y-8)(y-5)
(y-20)(y-2)
Answers
i'll give you the brainliest thingy if you'll help me
Answers
Answer:
[tex]\large \boxed{\text{1. B. $T_{{<6, -2>}}(QRST)$; 2. D. A$'$ (3,9), B$'$(4,0), C$'$(5,5)}}[/tex]
Step-by-step explanation:
1. Translation of Quadrilateral
A translation rule tells you how much to add to the values of x and y.
In your translation, the value of x increases from -5 to +1 — a distance of 6 units.
The value of y decreases from +4 to +2 — a distance of 2 units.
[tex]\text{The translation rule is $\large \boxed{\mathbf{T_\mathbf{{<6, -2>}}(QRST)}}$}[/tex]
2. Translation of triangle
The rule tells you to translate the triangle two units to the left and three units up, as in the second figure below.
A(5,6) ⟶ A'(3,9)
B(6,-3) ⟶ B'(4,0)
C(7,2) ⟶ C'(5,5)
The coordinates of the vertices of ∆A'B'C' are A'(3,9), B'(4,0), C'(5,5).
The length of the garden is 11 yards.The width of the garden is 8 yards. Select all of the expressions that chole could use to find the length of the fencing she will need
Answers
Answer:
The length of the fence is 38 yards
These are the expressions
1. Perimeter = 2l+ 2w
2. Perimeter = 2(l+w)
Step-by-step explanation:
This problem bothers on the mensuration of flat shapes, a rectangle.
The length of the fence is the perimeter of the garden which is the expression that Chole could use
1. Perimeter = 2l+ 2w
2. Perimeter = 2(l+w)
Given data
Length = 11 yards
Width = 8 yards
Perimeter = 2(11)+ 2(8)
Perimeter = 22+16
Perimeter = 38 yards
You’ll get a easy 15 points for answering this
Answers
Answer:
$50.73Step-by-step explanation:
NOTE:__________________________________________
applying a sales tax of 8% on an item means multiplying its original price by (1+8%).__________________________________________
The needed amount of money:
29.99×(1+8%)+16.99×(1+8%)
= 29.99×(1+(8÷100))+16.99×(1+(8÷100))
= 50.7384
:)
Easy question, Easy points LIMTED TIME. LOTS OF POINTS
Topic: Volume
Just need the answer
Answers
Answer:
Volume = PI * r^2 * height
Volume = PI * 3.5^2 * 2
Volume = PI * 12.25 * 2
Volume = 76.969020013 cubic meters
Step-by-step explanation:
Answer:
Volume = 76.969020013 m^3
Step-by-step explanation:
What is 60% of 52? (SHOW WORK)
Answers
Answer:
31.2
Step-by-step explanation:
To work out 60% of 52 you would first need to find 10%. You can do this by dividing 52 by 10, this gives you 5.2.
The final step is to multiply 5.2 by 6, this gives 31.2. This is because in order work out 60% you multiply 10% by 6.
1) Divide 52 by 10.
[tex]52/10=5.2[/tex]
2) Multiply 5.2 by 6.
[tex]5.2*6=31.2[/tex]
y−4=−2(x+3) Complete the missing value in the solution to the equation (-3, )
Answers
....
Answer:
y=4
Step-by-step explanation:
y-4=-2(x+3)
y-4=-2(-3+3)
y-4=-2.0
y-4=0
y=4
PLEASE HELP I DONT UNDERSTAND THIS QUESTION!
Answers
Answer:
I think its D, hope its right
what is the value of x
Answers
Answer:X. The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable, but we can work out its value if we try!
A student has a one-dollar bill, a five-dollar bill, and a ten-dollar bill in a box. The student selects a bill from the box 45 times and selects the ten dash dollar bill 28 times. What formula should be used to calculate the experimental probability? What is the experimental probability of selecting the ten dash dollar bill? What is the theoretical probability of selecting the ten dash dollar bill?
Answers
Answer:
r / n
62.2%
33.3%
Step-by-step explanation:
The formula to be used is to divide the number of times that it came out by the total number of times the event was repeated because this was the experiment that was carried out, therefore this would be the experimental formula:
r / n
r = specific event (that the 10 dollar bill comes out)
n = total events
To calculate, we know the previous values r = 28 and n = 45, we replace:
28/45 = 0.622
that is, 62.2% is the experimental probability.
To calculate the theoretical propagation, we know that there are 3 types of banknotes and we want 1 of those 3 types to appear, therefore:
1/3 = 0.333
Ie 33.3% is the theoretical probability
Identify the constant of proportionality
y=2x+2
Answers
Answer:
2 is the constant of proportionality
Step-by-step explanation:
we look at the linear function y = 2x + 2
You ask for the constant of proportionality.
y related to x
y = 2 * (x + 1)
y/(x + 1) = 2
2 is the constant of proportionality
I NEED HELP NOW!!!!!! Kelly is 6 times as old as Michael and 13 years older than Lucy. The sum of their ages is 91.
How old is each person?
Answers
Answer:
Kelly: 48
Michael: 8
Lucy: 35
Michael: 8
Lucy: 35
is this correct? please answer
Answers
Answer:
Yes, letter D is correct.
Step-by-step explanation:
The shape is a trapezoid so you'll have two congruent pairs of base angles.
An electronic company has 450 employees. The company plans to increase its staff by 30%. How many new employees will the company hire?
Answers
Answer:
135 new employees, 585 total employees
Step-by-step explanation:
Find 30% of 450.
(you can use any variables)
a = p*w
a = .30*450
a = 135
The company will hire 135 new employees, which would be (450 + 135) 585 total employees.
hope this helps :)
135 new employees should be hired by company to increase 30% of the employees.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
The number of employees in electronic company is 450.
The company plans to increase its staff by 30%
We need to find the number of employees to be hired by company.
30% of 450
Thirty percentage of four hundred fifty.
Convert 30% to decimal value by dividing with 100.
30/100=0.3
Now multiply 0.3 with 450
0.3×450
One hundred thirty five.
135
Hence, 135 new employees should be hired by company to increase 30% of the employees.
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A)125
B)130
C)120
D)135
Answers
Answer:
The answer is B.
Step-by-step explanation:
Pentagons have a sum of 540°
540 - (115 + 115 + 90 + 90)
540 - 410
130
Answer:
B)130
Step-by-step explanation:
115+115+90+90=410
pentagon angles add up to 540
410+130=540 degrees
Identify the triangle that contains an acute angle for which the sine and cosine ratios are equal.
Triangle A B C has angle measures 50 degrees, 40 degrees, and 90 degrees.
Triangle A B C has angle measures 45 degrees, 45 degrees, 90 degrees. The lengths of sides A C and C B are congruent.
Triangle A B C has angle measures 68 degrees, 22 degrees, and 90 degrees.
Triangle A B C has angle measures 60 degrees, 30 degrees, and 90 degrees.
Answers
Answer:
Step-by-step explanation:
Given that, a series of triangle,
For the sine and cosine to be equal, then,
Sinθ = Cosθ
From, trigonometry identities
Sinθ = Cos(90-θ)
Then,
θ = 90-θ
θ + θ = 90
2θ = 90
θ = 90 / 2
θ = 45°
From the triangle given, using trigonometry ratio,
Sinθ = opposite / hypotenuse.
Sinθ = 20 / 25
Sinθ = 0.8
θ = arcsin(0.8)
θ = 53.13°
The other angles at the triangle is
90-53.13 = 36.87°.
Answer:
b
Step-by-step explanation:
Y=3^x graph and table
Answers
Which line has the greatest rate of change? A line passing through (-1, 4) and (1, 7). A line passing through (1, 3) and (5, 11). A line passing through (1, 1) and (4, -3). A line passing through (0, 6) and (12, 9). please help!!
Answers
Answer:
A line passing through (1, 3) and (5, 11)
Rate of change = 2
Step-by-step explanation:
Rate of change = change in y / change in xr = Δy/ΔxLet's get the rate of change for each line:
A line passing through (-1, 4) and (1, 7).
r = (7 - 4) / (1 -(-1)) = 3/2A line passing through (1, 3) and (5, 11).
r = (11 - 3) / (5 - 1) = 8/4 = 2A line passing through (1, 1) and (4, -3).
r = (- 3 - 1) / (4 - 1) = -4/3A line passing through (0, 6) and (12, 9)
r = (9 - 6) / (12 - 0) = 3/12 = 1/4Comparing the values of r, we can see the greatest one is 2 for the line passing through (1, 3) and (5, 11)
Please help me now plz
I will mark you brainliest
Answers
Answer:
155.9 = h
Step-by-step explanation:
Since it is an equilateral triangle, the angles are all 60 degrees
Call the angle on the bottom right theta
Theta = 60 degrees
The angle h makes with the base is 90 degrees so it is a right triangle
sin theta = opp/ hyp
sin 60 = h/ 180
Multiply each side by 180
180 sin 60 = h
155.8845727 = h
To the nearest tenth
155.9 = h
Two sides of the triangle that form a 90 degree angle are called the
Answers
Answer:
The two sides of the triangle that are by the right angle are called the legs
Step-by-step explanation:
Answer:
Step-by-step explanation:
The two sides of the triangle that are by the right angle are called the legs... and the side opposite of the right angle is called the hypotenuse
2x2x2x2x2x2x2x2x2x2=?
Answers
Answer:
1024
Step-by-step explanation:
calculators are good resources when its math
A boy holding a stack of 9 identical books steps on a scale and weighs 138 pounds. The boy then holding a stack of 3 of the same books again steps on the scale and weighs 120 pounds. How much does the boy weigh?
Answers
Answer:
111 pounds
Step-by-step explanation:
A boy holding a stack of 9 identical books steps on a scale and weighs 138 pounds.
If the boy's weight is represented as B and the books are represented as b, this implies that:
B + 9b = 138
The boy then holding a stack of 3 of the same books again steps on the scale and weighs 120 pounds. This implies that:
B + 3b = 120
This has yielded two simultaneous equations:
B + 9b = 138
B + 3b = 120
We can solve by subtracting the second from the first.
B + 9b = 138
- (B + 3b = 120)
-----------------------
=> 6b = 18
b = 18 / 6 = 3 pounds
This means that each book weighs 3 pounds.
Putting b back in the second equation:
B + (3 * 3) = 120
B + 9 = 120
B = 120 - 9
B = 111 pounds
Therefore, the boy weighs 111 pounds.
Answer:
The boy would weigh 111 lbs.
Explanation:
Its complicated
What is the equation of the graph below?
Answers
Answer:
y = sin(x+90)
Step-by-step explanation:
The shape of the graph shown is a y = cos x graph
Since that is not an option, we know that it must be translated somewhat
Sin x and cos x graphs are the exact same in shape, but differ by 90°
Y = sin (x+90) is the same as a Y = cos x graph, so Y = sin(x+90) is our answer
Answer:A
Step-by-step explanation:
I did it rn
Mr. Jones buy 6 packages of pencils. There are 8 pencils in each package. How many pencils does Mr. Jones buy?
Answers
Answer:
Mr. Jones buys 48 Pencils.
Step-by-step explanation:
6x8=48
Step-by-step explanation:
48 pencils.
If there is 6 packages of pencils, and there is 8 pencils in each, then you multiply 6 x 8 to get 48 pencils.
I hope this helped.
What is the volume of the can below? Use = 3.14 and round your answer to the nearest tenth.
66 mm
96 mm
cubic millimeters
Answers
The volume of the can is 328, 268. 16 mm³.
What is Volume?Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies.
The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
We have,
Radius = 66/ 2= 33 mm
Height= 96 mm
So, volume of Can
= πr²h
= 3.14 x 33² x 96
= 3.14 x 1,089 x 96
= 328, 268. 16 mm³
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Please help i never learned this
chapter 8 question 6
Answers
Answer:
0.73
Step-by-step explanation:
[tex] \tan \: 36 \degree =0.726542528 \\ \tan \: 36 \degree =0.73 \\ [/tex]
What is the LCM of 30 and 35?
Answers
Answer: 210
Explanation: To find the least common multiple for the integers 30 and 35, we start by making a factor tree for each of our integers.
So 30 is 10 · 3 and 10 is 5 · 2.
35 is 7 · 5.
Notice that our 5's match up as factors of each of our integers.
When finding the least common multiple, we simply multiply all of our factors together but since the 5's match up,
we only multiply by a 5 once.
So our least common multiple or LCM is
5 · the 2 that doesn't match up · the 3 that
doesn't match up · the 7 that doesn't match up.
So we have 5 · 2 · 3 · 7 or 210.
Work is shown below.
Gavin mixes the amount of red from one shade of paint with the amount of yellow from a different shade of paint. He mixes the batch so he will have the greatest possible amount of paint. What amounts of red and yellow from which shades are used in the mixture?
Answers
Answer:It would be 3 1/4 from sunrise, yellow and 5 5/6 red from mango.
Gavin should mix equal amounts of the primary colors red and yellow to achieve the greatest possible amount of orange paint through subtractive color mixing.
Explanation:Gavin is looking to mix paint to create the greatest possible amount of a new paint color. To do this, he should use the primary colors red and yellow to make the secondary color orange. When mixing paints, which is a form of subtractive color mixing, combining these two pigments will result in a new hue without diminishing the amount of paint he has.
In subtractive color mixing, the secondary color orange is created by mixing the primary colors red and yellow in equal proportions. To obtain the largest amount of new paint, Gavin should mix equal parts of the red and yellow shades, assuming that the volumes of paints being mixed are also equal. Thereby, making use of the entire quantity of red and yellow paint to create the largest possible amount of orange paint.
It's important to note that this approach is different from additive color mixing, which involves light colors and operates under a different set of rules. In Gavin's scenario with pigments, red and yellow are the primary colors he should focus on to achieve the desired outcome.