100 POINTS!!!!!!!
Part A: What is a coterminal angle of θ such that 0 ≤ θ ≤ 2π?
Part B: What are the exact values of all six trigonometric functions evaluated at θ?
Answers
Answer:
A. coterminal angle = 4π/3
B. sin(θ) = -√3/2; csc(θ) = -2√3/3; cos(θ) = -1/2;
sec(θ) = -2; tan(θ) = √3; cot(θ) = √3/3
Step-by-step explanation:
A.Any angle that is a multiple of 2π added to the given angle will be coterminal. You want one in the range [0, 2π], so we need to add 4π to the given angle
coterminal angle = -8π/3 +4π = -8π/3 +12π/3
coterminal angle = 4π/3
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B.The reference angle is 4π/3 -π = π/3. θ is a quadrant III angle, so both the sine and cosine are negative.
sin(θ) = -√3/2 . . . csc(θ) = -2√3/3
cos(θ) = -1/2 . . . sec(θ) = -2
tan(θ) = √3 . . . cot(θ) = √3/3
Related Questions
please answer and use statement reason
Answers
Answer:
x = 15
Step-by-step explanation:
FD and AC are parallel because both are perpendicular to EB. Angle EDF and Angle DCA are congruent because they are corresponding angles. The measure of Angle DCA is also 3x because congruent angles have the same measure.
Now consider Triangle ACD. Because the sum of all three measures of the angles in a triangle add up to 180°.
x + 8x + 3x = 180°
12x = 180°
12x/12 = 180/12
x = 15
A rock is dropped from the top of a building and hits the ground at a velocity of −72ft/sec. If the acceleration due to gravity is −32ft/sec^2, what is the height of the building?
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solve the formula P = 2l + 2w for w.
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We are given the following equation :
[tex]{:\implies \quad \sf P=2L+2w}[/tex]
And we need to solve for w, so let's start :
[tex]{:\implies \quad \sf P=2L+2w}[/tex]
Now, transpose 2L to LHS ;
[tex]{:\implies \quad \sf P-2L=2w}[/tex]
[tex]{:\implies \quad \sf 2w=P-2L}[/tex]
[tex]{:\implies \quad \boxed{\bf{w=\dfrac{(P-2L)}{2}}}}[/tex]
Hence, Option a) is correct
Can someone help me out!
Answers
Answer:
option c
Step-by-step explanation:
This is the net of square pyramid.
Base of the square pryamid is square and all the other face are triangle.
find the e measure of the missing angle. round to 2 decimal places
Answers
Answer:
theta= 1.085
Step-by-step explanation:
y by the power of 2 + 4=20
Answers
Answer:
y is equal to 4 if that's what ur asking for
Answer:
16 if ur asking for y^2+4=20
Step-by-step explanation:
Kim is 15 years old. Her father is 4 times as old as her now. In how many years time their total age be 115 years.
Answers
Answer:
20 years time
Step-by-step explanation:
Taylor buys necklaces at wholesale for her store for $6, then she adds a mark up of
120% to the wholesale cost she paid for the necklaces. What is the sale price of
necklaces at Taylor's store?
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Cost is 6 USD
Selling price is 6 + markup
Markup = 6 * 120 /100 put this expression and check again selling price
Selling price = 6 + (6 * 120) / 100
= 13,2 usd
Find the roots of p(x)=x^3-10x^2+25
Answers
Answer:
{−1.47596288535, 1.73968983949, 9.73627304586}
Step-by-step explanation:
The roots of this cubic are real and irrational, as indicated by a graph of it. (Rational roots would be divisors of 25.) The same graphing calculator can provide an iterative solution to 12 significant figures. Here, we have used Newton's method iteration. The iteration function is ...
g(x) = x -p(x)/p'(x) . . . where p'(x) is the derivative: 3x^2-20x
We started each iteration using the value shown on the graph.
x ∈ {−1.47596288535, 1.73968983949, 9.73627304586}
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The second attachment shows another calculator's solution. The values of x that are roots are the opposite of the constant in each binomial factor. You will notice this solution has a couple more significant figures than the one shown above.
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Additional comment
There are several formulas for finding the "exact" roots of the cubic. Here's a trig approach that works reasonably well for cubics with 2 or 3 real roots.
We can define, for p(x) = x³ +ax² +bx +c, ...
s = -a/3 = 10/3
t = b -a²/3 = -100/3
r = a(2a² -9b)/27 +c = -10(200)/27 +25 = -1325/27
d = √(-4t/3) = √(400/9) = 20/3
h = 4r/d³ = -53/80
Now, the roots are ...
x = s +d·sin(arcsin(h)/3 +2nπ/3) . . . . for n=-1, 0, 1
= 10/3 +20/3·sin(arcsin(-53/80)/3 + n(2π/3)) . . . . . "exact solution"
= (10/3)(1 +2·sin(-13.8303° +n(120°))
= -1.47596..., or 1.73969..., or 9.73627...
160° А C B What is the mŁABC ?
Answers
[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer☂}}[/tex]
By theorem : Angle made by an arc at the centre is double the angle made by the same arc on the circumference part of the circle.
Therefore~
[tex]\qquad \sf \dashrightarrow \: 2 \times \angle ABC = 160[/tex]
[tex]\qquad \sf \dashrightarrow \: \angle ABC = 160 \div 2[/tex]
[tex]\qquad \sf \dashrightarrow \: \angle ABC = 80 \degree[/tex]
I hope you understood ~
A card is drawn at random from a standard deck of playing cards (no jokers). If the card is a spade, the player wins $7; if it is not a spade, the player loses $1.
What is the expected value of this game? $________________
Answers
The expected value of the game is the mean value of the game
The expected value of the game is $1
How to determine the expected value?There are 13 spades in a deck of card of 52
So, the probability of selecting a spade is:
P(Spade) = 13/52
Simplify
P(Spade) = 1/4
Winning = $7
The probability of not selecting a spade is:
P(Not spade) = 1 - 1/4
Simplify
P(Not spade) = 3/4
Lose = $1
The expected value of the game is:
[tex]E(x) = \sum x * P(x)[/tex]
This gives
[tex]E(x) = \frac 14 * 7 - 1 * \frac34[/tex]
Simplify
[tex]E(x) = \frac 74 - \frac34[/tex]
Evaluate
[tex]E(x) = 1[/tex]
Hence, the expected value of the game is $1
Read more about expected values at:
https://brainly.com/question/15858152
What is the value of x?
Enter your answer in the box.
X
8 2
X=
30°
452
Answers
The length οf the perpendicular is 2√2.
What is Trigοnοmetry?Trigοnοmetry is a branch οf mathematics that deals with the study οf relatiοnships between the sides and angles οf triangles. It includes the study οf trigοnοmetric functiοns such as sine, cοsine, and tangent, which are used tο sοlve prοblems in fields such as engineering, physics, and navigatiοn.
Step 1:
Let's call the length οf the perpendicular "p".
Frοm the given infοrmatiοn, we knοw that the hypοtenuse is 8√2 and the angle at the base is 30 degrees. We can use trigοnοmetry tο find the length οf the perpendicular.
In a right triangle, the sine οf an angle is defined as the length οf the side οppοsite the angle divided by the length οf the hypοtenuse. Sο we have:
sin(30°) = p/8√2
We can simplify this expressiοn by nοting that sin(30°) = 1/2 and 8√2 = 8√(2/2) = 8√(1/√2) = 8/√2. Substituting these values, we get:
1/2 = p/(8/√2)
Simplifying further, we can multiply bοth sides by 8/√2:
4/√2 = p
Tο express the result in simplest radical fοrm, we can ratiοnalize the denοminatοr by multiplying the numeratοr and denοminatοr by √2:
p = 4/√2 * √2/√2 = 4√2
Therefοre, the length οf the perpendicular is 4√2.
Step 2:
Let's call the length οf the perpendicular "p".
Frοm the given infοrmatiοn, we knοw that the hypοtenuse is 4√2 and the angle at the base is 45 degrees. We can use trigοnοmetry tο find the length οf the perpendicular.
In a right triangle, the sine οf an angle is defined as the length οf the side οppοsite the angle divided by the length οf the hypοtenuse. Sο we have:
sin(45°) = p/4√2
We can simplify this expressiοn by nοting that sin(45°) = √2/2 and 4√2 = 4√(2/2) = 4√(1/√2) = 4/√2. Substituting these values, we get:
√2/2 = p/(4/√2)
Simplifying further, we can multiply bοth sides by 4/√2:
2√2 = p
Therefοre, the length οf the perpendicular is 2√2.
To learn more about Trigonometry from the given link
https://brainly.com/question/24349828
#SPJ1
The question is in the screenshot!
Answers
Answer:
5/2
Step-by-step explanation:
Phase shift refers to the sin graph movement left or right.
We would have to set x to 1, so factor out the 2.
(2x-5)-> 2(x-5/2)
From this, the phase shift would be 5/2 to the right.
. Find the angle between the given vectors to the nearest tenth of a degree. u = <2, -4>, v = <3, -8> (2 points)
Answers
Answer:
6.0
Step-by-step explanation:
practice many times
Ron has a co-op in the Astor Cooperative development. There are 40,000 shares in the cooperative ownership. If Ron owns 500 shares, what percentage of the cooperative corporation does he own?
Answers
Answer:
Ron owns 1.25% of shares.
Step-by-step explanation:
400/50000 comes out to 0.0125 which can be converted into a decimal by moving the decimal two places to the right.
Solve each of the following equations. Show its solution set on a number line. Check your answers. 3(x-2)=12
PLS HELP WILL GIVE BRAINLIEST
Answers
x = 6
Step-by-step explanation:
[tex]\sf3(x - 2) = 12 \\ \sf3x - 6 = 12 \\\sf3x = 12 + 6 \\ \sf3x = 18 \\ \sf \: x = \frac{18}{3} \\ \sf \: x = 6[/tex]
Answer: (negative solution): x=-2, (positive solution): x=6
What is the quotient of 2x3 + 3x2 + 53 - 4 divided by 22 +1 +1?
2x +1+
2- - 5
2 +2+1
22 +1+
2.1 - 1
2 +2+1
2x +1+
4z - 4
++1
21 +5+ 12 +1
2+2+1
Answers
Answer:
42
Step-by-step explanation:
Rewrite the fraction in the sentence below as a percentage. At a certain wedding, 1/10 of the guests were over 60 years old.
Answers
Answer:
10%
Step-by-step explanation:
1/10 = 10%
170 What is the mZBAC?
Answers
Answer:
m<BAC = 85°
Step-by-step explanation:
The measure of an inscribed angle is half the measure of its intercepted arc.
m<BAC = 170°/2
m<BAC = 85°
4 3/5 - 4/5 = ?
please explain it
ixl
Answers
Answer:
[tex] \frac{19}{3 } \: or \: 3 \frac{4}{5} [/tex]
Step-by-step explanation:
Change the mixed number into a regular fraction.
[tex] \frac{23}{5} - \frac{4}{5} [/tex]
Subtract the numerator.
[tex] \frac{19}{5} [/tex]
As a mixed number:
[tex]3 \frac{4}{5} [/tex]
a man buys a vehicle at a cost prize of R60 000 from Cape Town. He transported the vehicle from cape town to Gauteng province, where he stays, at a cost prize of R4 500. at what prize must he sell the car to make an overall profit of 25% ?
Answers
Answer:
R80625
Step-by-step explanation:
Total Cost : 60000 + 4500 = 64500
To make 25% profit: 64500 X 1.25 = 80625
Is the table linear or exponential?
Answers
Answer:
this table is linear
Step-by-step explanation:
there is a difference of 4 each time
Answer:
linear
Step-by-step explanation:
the difference in x and y values is constant
Tim had 85$ to spend on 6 books. After buying them he had 13$. How much did each book cost. Write using two step equations
Answers
Answer:
he spent 12 dollars on each book
Step-by-step explanation:
minus 13 from 85 you get 72 and then divide 72 by 6
Answer:
12$ each
Step-by-step explanation:
Tim had 85$ to spend on 6 books.
After buying them he had 13$.
85$ - 13$ = 72$How much did each book cost.
72$ / 6books = 12$ each bookThe length of the base of an isosceles triangle is x. The length of a leg is 2x - 2. The perimeter of the triangle is 71. Find
Answers
Answer:
x = 15
Step-by-step explanation:
x + 2x - 2 + 2x - 2 = 71
Solve for x, you get 15.
can someone help me with this math problem please
Answers
Answer: A (-7,-4)
Step-by-step explanation:
Took the same test
A circular sinkhole has opened near an intersection. The four corners of the intersection are occupied by a grocery store, a dollar store, a gas station, and a restaurant, and each corner contains part of the sink hole. The grocery stores property has 2/3 of the angle in the intersection at the dollar store has, but has 5° more of the sinkhole edge to stabilize. The gas station has the same angle on the intersection at the dollar store and 88° more edge To stabilize. What is the measure of the arc of the sinkhole that falls within the restaurants property?
Answers
The measure of the arc of the sinkhole that falls within the restaurants property is -21°
Measure of angles subtendedLet x be the angle at the dollar store at the intersection
Now the angle of the grocery store at the intersection, y is 2/3 that of the dollar store. So, y = 2x/3
Since both x and y are supplementary,
x + y = 180°
x + 2x/3 = 180°
5x/3 = 180°
x = 180° × 3/5
x = 36° × 3
x = 108°
Angle subtended by gas station at sinkholeThe gas station has the same angle at the intersection but has 88° more of the sinkhole edge to stabilize. So, the angle the gas station store subtends at the sinkhole is z = x + 88°
Angle subtended by grocery store at sinkholeAlso, since the grocery stores property has 2/3 of the angle in the intersection at the dollar store has, but has 5° more of the sinkhole edge to stabilize. The angle the grocery store subtends at the sinkhole is k = y + 5° = 2x/3 + 5°
Measure of arc subtented by restuarantLet k' be the angle subtended by the restuarant at the sinkhole.
Since the sinkhole is a circle, we have that
x + z + k + k' = 360°
x + x + 88° + 2x/3 + 5° + k' = 360°
8x/3 + 93° + k' = 360°
8x/3 + k' = 360° - 93°
8x/3 + k' = 267°
So, making k' subject of the formula, we have
k' = 267° - 8x/3
Substituting the values of the variables into the equation, we have
k' = 267° - 8 × 108°/3
k' = 267° - 288°
k' = -21°
So, the measure of the arc of the sinkhole that falls within the restaurants property is -21°
Learn more about measure of arc here:
https://brainly.com/question/16916082
Rotate the given triangle 180° counter-clockwise about the origin. [ 0 -3 5 ] [0 1 2]
Answers
Answer:
[tex]\left[\begin{array}{ccc}0&3&-5\\0&-1&-2\end{array}\right][/tex]
Step-by-step explanation:
Rotation 180° (in either direction) about the origin causes each coordinate to have its sign changed. Effectively, the coordinate matrix is multiplied by -1.
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Additional comment
This is equivalent to reflection across the origin.
3 - 5
-1 -2
Cool scoops ice cream shop offers 60 different one topping sundaes. If there are different flavors of ice cream toppings and containers to hold the ice cream which of the following would not be the possible number of each category?
Answers
Answer:
I'm so confused. I don't get the question. I know the options are:
A) 3,4, 5
B) 2, 10, 4
C) 2, 10, 3
D) 2, 15, 2
but I don't understand the question. Could you maybe be a bit more specific?
How do you solve this problem?
Answers
Answer:
16 triangles I am pretty sure.
Step-by-step explanation:
Find the coordinates of the vertex for the parabola defined by the given quadratic function.
f(x) = 2x² – 20x +7
The vertex is
(Type an ordered pair.)
Answers
Answer:
(5, -43)
Step-by-step explanation:
The value of the x-coordinate of the vertex of a function in standard form is given by -b/2a. The value of a is the coefficient of the x^2 term. The value of b is the coefficient of the x term. In this problem, a = 2 and b = -20. When you evaluate -b/2a you would replace the b with -20 and replace the a with 2 so you get -(-20)/2(2) so the value of x is 5. Determine the value of y by evaluating f(5) = 2(5)^2 - 20(5) +7.