Use the unit circle to evaluate the six trigonometric functions of θ = -π.
Sin θ=
Cos θ=
Tan θ=
Csc θ=
Sec θ=
Cot θ=
Answer:
sin=0
cos=-1
tan=0
csc=undefined
sec=-1
cot=undefined
Step-by-step explanation:
On the unit circle, [tex]-\pi=\pi[/tex]. The sin of theta is therefore 0, the cosine is -1, and the tangent is 0/-1=0. Since the following functions are just the reciprocals of the previous ones, the cosecant is 1/0=undefined, the secant is 1/-1=-1, and the cotangent is 1/0= undefined. Hope this helps!
All six trigonometric ratios were calculated using a unit circle and comes out to be
[tex]sin(-\pi )= -sin\pi =0\\cos(-\pi )= cos\pi =-1\\tan(-\pi )= -tan\pi=0 \\cosec(-\pi )= -cosec\pi =infinity\\sec(\pi )= sec\pi =-1\\cot(-\pi )=-cot\pi=infinity[/tex]
I have attached a unit circle diagram.
What is a unit circle in trigonometry?In this unit circle corresponding values of sine and cosine have been written near the angle 'α' in form (cosα,sinα)
x-coordinate is cosα
y-coordinate is sinα
now,
one can find other trigonometric ratios
[tex]tan\alpha =\frac{sin\alpha }{cos\alpha } \\\\cot\alpha =\frac{1}{tan\alpha } \\\\cosec\alpha =\frac{1}{sin\alpha } \\\\sec\alpha =\frac{1}{cos} \\[/tex]
Hence, we can find the rest of the trigonometric ratios by using the coordinates (cosα,sinα) for a particular angle 'α'.
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What is the greatest common factor of 9 and 14?
Answer:
1
Step-by-step explanation:
The factors of 9 are 9, 3, 1The factors of 14 are 14, 7, 2, 11 is the only number that can be divided into 9 and 14 without a remainder.The greatest common factor GCF of 9 and 14 is 1.
What is the greatest common factor of the given numbers?Given the numbers in the question:
9 and 14
To find the greatest common factor of two numbers, we need to identify all the factors of each number and then determine the greatest number they have in common.
First:
Factors of 9 are 1, 3, and 9, as these are the whole numbers that divide 9 without leaving a remainder.
Next,
Factors of 14 are 1, 2, 7, and 14, as these are the whole numbers that divide 14 without leaving a remainder.
The common factors of 9 and 14 are 1 since it is the only number that divides both 9 and 14.
Therefore, the greatest common factor of 9 and 14 is 1.
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Can someone help me please
Answer:
Step-by-step explanation:
Which is greater, 4.87 x 109 or 9.212 x 108?
Answer:9.212 x 108 is greater
Step-by-step explanation:4.87 x 109 =530.83
9.212 x 108 = 994.896
Which shows how 9.212 x 108 has a greater outcome than 4.87 x 109
Jeff collected 100 baseball cards. Thirty-three of the cards are Cincinnati Reds players, and 22 of them are Cleveland Indians. Part B What decimal represents the part of the cards that are neither Cincinnati Reds nor Cleveland Indians?
Answer:
0.45.
Step-by-step explanation:
To find the solution to this question, we will first need to determine how many cards are neither Cincinnati Reds and Cleveland Indians. We can do this by:
100 - 22 - 33 = 45. This is the number of cards that are neither the two teams.
To convert this to a decimal, simply divide by 100, giving us:
45 ÷ 100 = 0.45.
A university's freshman class has 5000 students. 90% of those
students are majoring in Economics. How many students in the
freshman class are Economics majors?
Answer:
4,500
Step-by-step explanation:
To find the number of students majoring in economics, you must turn 90% into a decimal making it .9.
Then you multiply the decimal to how many students there are (5000x.9) and that gives you 4,500.
18 - 3 x 2/ 5-1 squared
Answer:-3/5x(squared)+17
Step-by-step explanation:
Simplify and combine like terms
Find the number of digits in the square root of 61504.
Answer:
3
Explanation
There are 3 digits in the number 248 which is the square root of 61504.
√61504 = 248 --- 3 digits in 248
100) 4030
What’s the greatest common factor
Answer: 10
Step-by-step explanation:
100/10=10
4030/10=403
A soccer player uses her head to hit a ball up in the air from a height of 1 meters with an initial vertical velocity of 5 meters per second. The height h in meters of the ball is given by h = −4.9t2 + 5t + 1, where t is the time elapsed in seconds. How long will it take the ball to hit the ground if no other players touch it? Enter the time to two decimal places.
Answer:
It will take 1.19 seconds for the ball to hit the ground if no other players touch it
Step-by-step explanation:
The height of the ball after t seconds is given by the following equation:
[tex]h(t) = -4.9t^{2} + 5t + 1[/tex]
How long will it take the ball to hit the ground if no other players touch it?
This is t when h(t) = 0. So
[tex]-4.9t^{2} + 5t + 1 = 0[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
[tex]-4.9t^{2} + 5t + 1 = 0[/tex]
So [tex]a = -4.9, b = 5, c = 1[/tex]
So
[tex]\bigtriangleup = 5^{2} - 4*4.9*1 = 44.6[/tex]
[tex]t_{1} = \frac{-5 + \sqrt{44.6}}{2*(-4.9)} = -0.17[/tex]
[tex]t_{2} = \frac{-5 - \sqrt{44.6}{2*(-4.9)} = 1.19[/tex]
Since we want a time measure, the answer cannot be negative.
It will take 1.19 seconds for the ball to hit the ground if no other players touch it
PLZZZZ HELP WILL MARK BRAINLIEST IF CORRECT
8. While doing bicep curls, Tamara applies 155 Newtons of force to lift the dumbbell. Her forearm is 0.366 meters long and
she begins the bicep curl with her elbow bent at a 15° angle below the horizontal, in the direction of the positive x-axis.
Determine the magnitude of the torque about her elbow.
(Show work)
Answer:
54.8 Nm
Step-by-step explanation:
Torque is the cross product of the radius vector and force vector:
τ = r × F
Another way to write it is the product of the radius and force magnitudes times the sine of the angle between the vectors.
τ = rF sin θ
Here, r = 0.366 meters and F = 155 Newtons. F is in the +y direction, and r is 15° below the +x axis, so the angle between the vectors is 90° − 15° = 75°.
τ = (0.366 m) (155 N) (sin 75°)
τ = 54.8 Nm
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Let point C be on circle A. If ∠BAC 5 radians and segment BC is 12cm, what is the length of the radius
Answer:
2.4 cm
Step-by-step explanation:
The formula we would use
S = rθ
Where S = Arc length
θ = central angle in radians
r = radius of the circle or length of the radius.
From the question, we can see that if
If C = a point on circle A
The Segment BC = The arc length of the circle = 12cm
∠BAC = central angle in radians = 5 radians.
Since, S = rθ,
Length of the radius = S/θ
= 12cm/5 radians
Length of the radius = 2.4 cm
a circle has a center located at 2 5 and passes through the point 10 3 answer
Determine the equation of the circle. Show how you arrived at your answer.
Write the equation of the tangent line to the circle at the point . Show how you determined your answer.
Answer:
[tex](x-2)^{2} +(y-5)^{2} =\sqrt{68}[/tex]
Step-by-step explanation:
Givens
The center of the circle is at (2,5).A point on the circumference is at (10,3).First, we need to find the radius, which is the distance between the given points.
[tex]d=\sqrt{(3-5)^{2} +(10-2)^{2} } =\sqrt{4+64}=\sqrt{68}[/tex]
Therefore, the radius of the circle is
[tex]r \approx 8.25[/tex]
The explicit form of the equation of the circle would be
[tex](x-2)^{2} +(y-5)^{2} =\sqrt{68}[/tex]
Which equation can be used to solve for x?
Choose from the Equation Bank
Answer:
[tex]\frac{x-14}{2}=24[/tex]
Step-by-step explanation:
In the given figure two secants are intersecting outside the circle.
Angle formed by these secants = 24°
Measure of arcs intercepted = x° and 14°
Formula to get the unknown chord is,
24° = [tex]\frac{1}{2}(x-14)[/tex]
Therefore, equation (2) given in the equation bank will be used.
By further solving for the value of x,
24×2 = ( x - 14)
48 = x - 14
x = 48 + 14
x = 62°
Anne Deno purchased a house to fix up and use as a rental property. The house sold for $123,400. Anne made a $23,400 down payment and mortgaged the rest. Her annual expenses for mortgage interest, taxes, repairs, insurance, and depreciation totaled $8,750. Anne rented the house for $960 per month. What is the annual net income?
Answer:
The annual net income is $2770
Step-by-step explanation:
The annual net income on the rental property is the yearly rental minus the yearly annual expenses which consist mortgage interest,taxes, repairs,insurance as well as annual depreciation totaling $8,750
Annual rental =monthly rental* 12 months=$960*12=$ 11,520.00
Annual net income=$ 11,520.00-$8,750.00=$2,770
The annual net income is the gain that accrues to Anne Deno for purchasing the rental property and the subsequent letting to tenants
HELP PLEASE!!!! Both of the questions follow with the chart
Answer:
1. 0.75
2. 0.25
Step-by-step explanation:
Let's start off with number 1
There is only 2 answers that would make sense.
0.6 and 0.75
But only one is the answer
To find the answer you have to go to the columns that represent the equation
Then you divide
108/144
= 0.75
Now in number 2
You have to place the information in the graph where it corresponds and you get the numbers 24/96
Now divide
24/96
=0.25
Hope this helped :)
Have a good one!
Answer:
Let's denote:
probability that a person paid regular admission P(A)
probability that a person purchased no snack P(B)
probability that a person got discount on admission P(C)
probability that a person purchased snack P(D)
For picture 1
Applying Bayes theorem, we have:
probability that a person paid regular admission, given that person purchased no snack : P(A|B) = P(A ∩ B)/P(B) = (108/240)/(144/240) = 108/144 = 0.75
=> Option D is correct
For picture 2
As shown in picture, we have:
probability that a person got discount on admission and purchased snack:
P(C ∩ D) = 24/240 = 0.1
=> Option C is correct
Hope this helps!
:)
At an amusement park john wants to ride a rollercoaster that costs 19 tickets, a bumper car that costs 3 tickets, and a merry-go-round that costs 33 tickets. John had 31 tickets but lost 10 of them on a ride. How many more tickets does he need?
Answer:
John will need 34 more tickets to be able to go on all the rides he wants
Step-by-step explanation:
To solve this, we need to first of all know the total cost in terms of tickets of all the rides that john wants to have.
This will be
cost of roller coaster ride = 19 tickets
cost of bumper car ride = 3 tickets
cost of merry-go-round ride = 33 tickets
Total cost of rides = 19 + 3 + 33 =55 tickets
Next, we will need to find the number of tickets that John has left after losing 10 of them.
This will be 31 - 10 = 21 tickets left
To find the number of more tickets that John needs , we will subtract the number of tickets he has left from total ride ticket cost.
This will be 55-21 = 34 tickets.
Hence, John will need 34 more tickets to be able to go on all the rides he wants
use the rules of significant figures to simplify the following expression: 31.5 x 10.51
Answer:
31.5×10.51
315/10×1051/100
331065/1000
331.065
Sharon has a rectangular bedspread that measures 3 feet by 5 feet. She wants to
sew a fringe around the edge of the bedspread.
What length of fringe does Sharon need to purchase?
feet
Sharon gets a new bedspread that is 1.25 feet longer.
What length of fringe does Sharon need for the longer bedspread?
feet
Answer:
18.5
Step-by-step explanation:
The length of fringe Sharon needs to purchase is: 16 feet
If Sharon gets a new bedsheet of 1.25 feet longer, she will need a new length of fringe of: 18.5 feet
Recall:
Perimeter of a rectangular = 2(length + width)
Given the following:
length of Sharon's rectangular bedspread = 3 feetwidth of Sharon's rectangular bedspread = 5 feetThe length of fringe Sharon will need to purchase = perimeter of Sharon's rectangular bedspread
Perimeter = 2(3 + 5) = 16 feet
For a new bedspread that is 1.25 feet longer, she would get the following length of fringe:
Length = 3 + 1.25 = 4.25 feet
Width = 5 feet
New Perimeter = 2(4.25 + 5) = 18.5 feet
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what is the answer to 200% of 32?
Answer:
200% of 32 would be : 32 x 200/100 = 32 x 2 = 64
Hope this helps!
:)
Answer:
64
Step-by-step explanation:
When you want to know the 200% of a number just simply multiply it by 2.
In general, if you were to face with questions like this, just remove the zeros in the percentage and multiply.
200% of 32
2 × 32 = 64
Mr. Chandra drives to and from work each weekday. His trip is 15 miles one way. How many miles does he drive to and from work each week?
Answer:
150 is the answer I hope it helps
Answer:
150 miles
Step-by-step explanation:
15 x 2 x 5 = 150
2 times a day for 5 days
Rewrite the function by completing the square.
h(x)=4x^2-36x+81
Answer:
y = 4 (x - 9/2) +0
Step-by-step explanation:
hope ot helps you
Answer:
here
Step-by-step explanation:
Note: The monthly loan payment was calculated at 119 payments of $330.38 plus a final payment of $329.73. Loan Balance: $25,000.00 Loan Interest Rate: 10.0% Monthly Loan Payment: $330.38 Number of Payments: 120 Cumulative Payments: $39,644.95 Total Interest Paid: $14,644.95 On average, what dollar amount of each monthly payment is interest? $ What percent of the total payments is total interest? %
Answer:
Average monthly interest = $ 122.04
% total interest =36.94 %
Step-by-step explanation:
There are 120 cumulative payments and the total interest paid was $ 14,644.95.
Hence, the average monthly interest is :
Average monthly interest = $ 14,644.95 / 120
Average monthly interest = $ 122.04
% total interest
= ($ 14,644.95) / $ 39,644.95 x 100
% total interest =36.94 %
I need help with question 9 please
Answer:
The population is everyone listed in the city phone directoy; the sample is the 75 people selected
Step-by-step explanation:
Here is a probability scale:
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
There are 3 white counters and 2 black counters in a bag.
I take one of the counters at random.
Put a cross on the probability scale to show the probability
that I have chosen one of the white counters.
Answer:
see below
Step-by-step explanation:
You have 3 chances in 5 of drawing a white counter, so the probability is ...
3/5 = 0.6
Your mark will go at 0.6 on the probability scale.
Andrea brought $54.00 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was one-sixths as much as the sketchbook, and the sketchbook cost three-fourths the cost of the paint set. Andrea had $1.50 left over after buying these items.
Answer:
See explanation below
Step-by-step explanation:
In this case, I'm assuming you want to know the price of all items purchased by Andrea.
Let's gather all the data.
Andrea has initially 54$. From that she got a Brush (B), a sketchbook (S) and a paint set (P). At the end, she has a left over of 1.5$, so she actually spends 52.5$, and our first equation would be:
B + S + P = 52.5 (1)
Now, the B cost 1/6 as the S, and S was 3/4 the paint set, so oru equations here would be:
B = 1/6S (2)
S = 3/4P (3)
Now, according to this we can write the (1) expression in function of (2) and (3).
Replacing (3) in (2):
B = 1/6 (3/4P)
B = 3/24P
B = 1/8P (4)
And replacing (3) and(4) in (1) we have:
1/8P + 3/4P + P = 52.5
From here we can solve for P:
15/8P = 52.5
P = 52.5 * 8 / 15
P = 28.16$
Now we can replace this value to get the Sketchbook, and then, the brush:
S = 3/4 * 28.16
S = 21.12$
B = 1/6 * 21.12
B = 3.52$
These values would be the price of all items.
Help!
Thank you so much to whoever can help me!
Answer:
D for A then for B is C
Step-by-step explanation:
so if you calculate me but it is going to help you in this
Megan, Sally and Tom share £180 in the ratio 1:3:2 how much more does Sally recieve than Megan?
Answer: Sally recieves £60 more than Megan
Step-by-step explanation:
Add the ratio together 1+3+2=6
£180 divided by 6 = 30
Megan gets 30
Sally gets 30x3=90
Tom gets 30x2=60 30:90:69
(3/5)/2=(1/4)/x solve for x
Answer:
[tex]x=\frac{6}{5}[/tex]
Step-by-step explanation:
[tex]\frac{3}{5} / 2=\frac{3}{10}[/tex]
[tex]\frac{3}{10} =\frac{1}{4} x[/tex]
[tex]x=\frac{6}{5}[/tex]
Answer:
x=
[tex] \frac{5}{6} [/tex]
Step-by-step explanation:
(3/5)/2=(1/4)x
3/10=1/4x
12x=10
x=10/12=5/6
A flagpole is 10 m tall and has a shadow that is 7 m long. At the same time how tall is a nearby building if its shadow is 28m long?
Answer:
40m
Step-by-step explanation:
28÷7=4
10 x 4= 40