26. Given that tanθ almost equal to≈ 2.773 where 0<θ<π2, find the values of sinθ and cosθ. 27. Given that tanθ ≈ -1.559 where 3π2<θ<2π , find the values of sinθ and cosθ.

Answers

Answer 1

Answer:

a. i. sinθ = +0.941

ii. cosθ = +0.339

b. i. sinθ = -0.842

ii.  cosθ = +0.540

Step-by-step explanation:

a. Given that tanθ almost equal to≈ 2.773 where 0<θ<π/2, find the values of sinθ and cosθ.

i. sinθ

Given that 1 + cot²θ = cosec²θ

cotθ = 1/tanθ

Since tanθ = 2.773, cotθ = 1/tanθ = 1/2.773 = 0.3606

So, 1 + cot²θ = cosec²θ

1 + (0.3606)² = cosec²θ

1 + 0.13 = cosec²θ

1.13 = cosec²θ

cosec²θ = 1.13

cosecθ = ±√1.13

cosecθ = ±1.063

1/sinθ = ±1.063

sinθ = ±1/1.063

sinθ = ±0.9407

sinθ ≅ ±0.941

Since we have 0<θ<π/2, sinθ is in the first quadrant, so we choose the positive value.

So, sinθ = +0.941 where 0<θ<π/2

ii. cosθ

Given that 1 + tan²θ = sec²θ

Since tanθ = 2.773,

So, 1 + tan²θ = sec²θ

1 + (2.773)² = sec²θ

1 + 7.6895 = sec²θ

8.6895 = sec²θ

sec²θ = 8.6895

secθ = ±√8.6895

secθ = ±2.9478

1/cosθ = ±2.9478

cosθ = ±1/2.9478

cosθ = ±0.3392

cosθ ≈ ±0.339

Since we have 0<θ<π/2, cosθ is in the first quadrant, so we choose the positive value.

So, cosθ = +0.339 where 0<θ<π/2

b. Given that tanθ ≈ -1.559 where 3π/2<θ<2π, find the values of sinθ and cosθ.

i. sinθ

Given that 1 + cot²θ = cosec²θ

cotθ = 1/tanθ

Since tanθ = -1.559, cotθ = 1/tanθ = 1/-1.559 = -0.6414

So, 1 + cot²θ = cosec²θ

1 + (-0.6414)² = cosec²θ

1 + 0.4114 = cosec²θ

1.4114 = cosec²θ

cosec²θ = 1.4114

cosecθ = ±√1.4114

cosecθ = ±1.1880

1/sinθ = ±1.1880

sinθ = ±1/1.1880

sinθ = ±0.8417

sinθ ≈ ±0.842

Since we have 3π/2<θ<2π, sinθ is in the fourth quadrant, so we choose the negative value.

So, sinθ = -0.842 where 3π/2<θ<2π

ii. cosθ

Given that 1 + tan²θ = sec²θ

Since tanθ = -1.559,

So, 1 + tan²θ = sec²θ

1 + (-1.559)² = sec²θ

1 + 2.4305 = sec²θ

3.4305 = sec²θ

sec²θ = 3.4305

secθ = ±√3.4305

secθ = ±1.8522

1/cosθ = ±1.8522

cosθ = ±1/1.8522

cosθ = ±0.5399

cosθ ≈ ±0.540

Since we have 3π/2<θ<2π, cosθ is in the fourth quadrant, so we choose the positive value.

So, cosθ = +0.540 where 3π/2<θ<2π


Related Questions

Please answer this!!!

Answers

Answer:

so a = -1  b = -1/4  and c = 7

Step-by-step explanation:

-x^2 - 1/4x +7

This is in the form

ax^2 + bx +c

so a = -1  b = -1/4  and c = 7

Answer:

[tex]a=-1[/tex]

[tex]b=-\frac{1}{4}[/tex]

[tex]c=7[/tex]

Step-by-step explanation:

Hope this helps:)

Mindy puts a rectangular poster of her favorite singer on a wall in her bedroom. What is the perimeter of the poster?

Answers

Answer:

Step-by-step explanation:

PLSSS HELPP ASAP
Each of the following data sets has a mean of 5. Which has the greatest variability? (no calculations are necessary)
Α.{1, 3, 5, 7, 9}
В. {1, 1, 1, 1, 21}
с. {3, 4, 5, 6, 7}
D. {5, 5, 5, 5, 5)

Answers

Answer:

choose B is the greatest variablity

Need urgent help for this math question will give brainliest

Answers

Answer:

1st box: 6x - 3 = 9

2nd box: 6x = 12

3rd box: x = 2

4th box: y = 4(2) - 3

5th box: y = 8 - 3

6th box: y = 5

Step-by-step explanation:

Part A-

1) 4x-3 = -2x+9

2) 4x+2x -3 = -2x+2x + 9

3) 6x -3 = 9

4) 6x -3+3 = 9+3

5) 6x = 12

6) 6x/6 = 12/6

7) x = 2

Part B-

1) y=4x-3

2) y=4(2)-3

3) y=8-3

4) y= 5

Therefore, x = 2 and y = 5.

I really hope this helps, good luck!

On a unit circle, the terminal point of 0 is (sqrt3/2,1/2)

What is 0?

Answers

Answer:

The measure of [tex]\theta[/tex] is 30°.

Step-by-step explanation:

In the statement, the angle has been misrepresented. The corrected statement is described below:

"On a unit circle, the terminal point of [tex]\theta[/tex] is [tex]\left(\frac{\sqrt{3}}{2}, \frac{1}{2} \right)[/tex]. What is [tex]\theta[/tex]?"

The measure of the angle ([tex]\theta[/tex]), in radians, is in standard form, that is, it is done with respect to the +x semiaxis. The measure of the angle whose terminal point is of the form [tex](x,y)[/tex] is determined by the following inverse trigonometric function:

[tex]\theta = \tan^{-1}\left(\frac{y}{x} \right)[/tex] (1)

If we know that [tex]x = \frac{\sqrt{3}}{2}[/tex] and [tex]y = \frac{1}{2}[/tex], then the measure of [tex]\theta[/tex] is:

[tex]\theta = \tan^{-1} \frac{\sqrt{3}}{3}[/tex]

[tex]\theta = 30^{\circ}[/tex]

The measure of [tex]\theta[/tex] is 30°.

Answer:

its 60 degrees

Step-by-step explanation:

a p e x 2021

A test has several multiple choice questions, each with 5 choices. If you guess on 4 questions, what is the probability that you get all 4 correct

Answers

Answer:

4/20 or 1/5

Step-by-step explanation:

number of guesses/total possible outcomes (formula for this question since it is an independent event)

total possible outcomes: 4(# of questions) x 5(# of possible answers in 1 question)

total possible outcomes: 20

number of guesses: 4 x 1(there are 4 questions and you guess 1 answer for each question)

number of guesses: 4

number of guesses/total possible outcomes = 4/20 or 1/5

(I might be wrong lol, I haven't learned it in a long time)

Jane bought 6 dozen banana at $250per dozen. She sells four and a half dozen at $35 each and the other were sold at $20 each. Determine if she made a profit or loss state her profit or loss as a percentage. Show working

Answers

Answer:

87.5% loss

Step-by-step explanation:

6 • 250 = 1500

4.5 • 35 = 157.5

6 - 4.5 = 1.5

1.5 • 20 = 30

157.5 + 30 = 187.5

1500x = 187.5

x = 0.125

12.5% is an 87.5% decrease

In a carnival game, players get 5 chances to throw a basketball through a hoop. If 7 out of 20 players made all 5 baskets, how many players out of 400 would you expect to make all 5 baskets?

Answers

Answer:  140

=====================================================

Work Shown:

7/20 = 0.35 = 35% of the 20 players made all five baskets.

If this trend holds up, then we should expect 35% of the 400 people to make all five baskets.

35% of 400 = 0.35*400 = 140

We expect about 140 people will make all five baskets.

Note how 140/400 = 0.35 = 35%

-------------

Through another alternative method, we can solve like this

7/20 = x/400

7*400 = 20*x ... cross multiply

2800 = 20x

20x = 2800

x = 2800/20 ... dividing both sides by 20

x = 140 which is the same result as before

140

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Quadrilateral ABCD is inscribed in a circle. If angle B measures 112°, what is the measure of angle D?

Answers

Answer:

68°

Step-by-step explanation:

If a quadrilateral is inscribed in a cirle, the sum of its opposite angles is 180°. Angles B and D are opposite => B+D=180° => D=180°-B=180°-112°=68°

Answer:

68°

Step-by-step explanation:

Since angles B and D are opposite each other, they are supplementary.

what is the y-intercept of this quadratic?

Answers

Answer:

The y-intercept is the value at which the graph of the function intersects the y-axis. Every quadratic has a (single) y-intercept. The reason for this is that the y-intercept is the function value at x = 0, and we can always substitute x = 0 into the quadratic.

What is the value of x
A. 100 B.50 C.25 D.35

Answers

Answer:

D

Step-by-step explanation:

I believe this is correct

D.35. I’m pretty sure this is the correct answer as well

please help me im in need of serious help or ill flunk :(

Answers

Answer:

1. Interest: 15%

Amount owed: $500

2. Interest: 6%

Amount owed: $1,500

3. Interest: 18%

Amount owed: $12,500

4. Interest: 6%

amount owed: $5,000

Step-by-step explanation:

What is the slope of the line?
7x+2y=5

Answers

Answer:

- 7/2

Step-by-step explanation:

Given the points A(-3, -2) and B(6, 1), determine the coordinates of point P on directed line segment that partitions in the ratio 2/1.

Answers

Answer:

[tex]P = (3,0)[/tex]

Step-by-step explanation:

Given

[tex]A = (-3,-2)[/tex] ---- [tex](x_1,y_1)[/tex]

[tex]B = (6,1)[/tex] --- [tex](x_2,y_2)[/tex]

[tex]m:n =2:1[/tex]

Required

The coordinates of P

This is calculated as:

[tex]P = (\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}][/tex]

So:

[tex]P = (\frac{2*6+1*-3}{2+1},\frac{2*1+1*-2}{2+1})[/tex]

[tex]P = (\frac{9}{3},\frac{0}{3})[/tex]

[tex]P = (3,0)[/tex]

a article cost$1424 it may be purchased by depositing$560 and making monthly payment of 48 how many months are required to complete payment​

Answers

Answer:

18months

Step-by-step explanation:

1424-560=864

864÷48=18

Answer:

18

Step-by-step explanation:

$1424-$560= $864

$864 divided by $48 = 18 months

If I have 75 oranges and I eat two and a half everyday for 30 days how many will I have eaten in one month

Answers

Answer:

all 75 of them

Step-by-step explanation:

2.5(30) = 75

Two mechanics worked on a car. The first mechanic worked for 5 hours, and the second mechanic worked for 15 hours. Together they charged a total of $1025. What was the rate per hour by each mechanic if the sum of the two rates was $105 per hour?

Answers

Answer:

The mechanic who worked 5 hours charged $115 per hour, the one who worked 15 hours charged $120 per hour.

Step-by-step explanation:

x = rate of mechanic who worked 5 hours

y = rate of mechanic who worked 15 hours

Then

x + y = 235

5x + 15y = 2375

Just solve these 2 equations above for x and y.

x + y = 235 ⇒ x = 235 - y

Substitute into second equation to find y.

5(235 - y) + 15y = 2375

1175 - 5y + 15y = 2375

10y = 1200

y = 1200/10 = 120

x = 235 - y = 235 - 120 = 115

ABCD and EFGH are rectangles with AB=10cm ,BC=7cm ,EF=7cm and FG =4cm ,all figures accurate to the nearest cm . Find the largest possible value of the shaded area . *

Answers

Answer:

42 cm^2

Step-by-step explanation:

Please find attached an image showing the diagram

area of shaded part = area of larger rectangle - area of smaller rectangle

Area of a rectangle = length x width

larger rectangle = 10 x 7 = 70 cm^2

smaller rectangle = 7 x 4 = 28cm^2

Area of shaded part : 70 - 28 = 42cm^2

Which of the following graphs is described by the function given below?
y = x^2 - 6x - 16
A. Graph A
B. Graph B
C. Graph C
D. Graph D

Answers

Answer:

(C).Graph C

Step-by-step explanation:

The answer is graph c

What two numbers sum up to 11 and multiply to 18

Answers

Answer:

9 and 2

Step-by-step explanation:

9+2=11

9×2=18

Answer:

9 and 2

Step-by-step explanation:

Find the middle point, M, of ab

Answers

Distance from A to B = B-A = 18-0 = 18

M is the midpoint which means it is equal distance between A and B

M = distance between A and B divided by 2:

M = 18/2 = 9

Answer: M = 9

Answer:

9

Step-by-step explanation:

If m is a midpoint of AB

then

M = 1/2AB

If AB = 18

Then M = 1/2 of 18

18/2 = 9

Hence M = 9

What is the reciprocal of -3 2/7 ? -3 7/2 -23/7 -7/23 3 2/7​

Answers

Reciprocal of -32/7 = -7/32

Answer:

-32/7 = -7/32

Step-by-step explanation:

Ayuda con estos ejercicios Porfavor es para Mañana​

Answers

I know understood 3 and 4
3 - C
4 - B

Vince's birthday party is going to be at his favorite science museum next weekend. He has 8 friends who want to see the Dinosaur Discovery show and 4 friends who want to see the Wild Weather show. Typically, the Dinosaur Discovery show costs d dollars per ticket, and the Wild Weather show costs w dollars per ticket. But next weekend, all tickets are half price! Pick all the expressions that represent the total cost of his friends' tickets.

Answers

Answer:

See explanation

Step-by-step explanation:

Dinosaur Discovery show = 8 friends

Wild Weather show = 4 friends

Cost of Dinosaur Discovery show = $d

Cost of Wild Weather show = $w

At regular price:

Total cost of his friends' tickets = 8 * d + 4 * w

= 8d + 4w

At half price

Total cost of his friends' tickets =

8 * 1/2d + 4 * 1/2w

= 8/2d + 4/2w

= 4d + 2w

Total cost of his friends' tickets = 4d + 2w

can anyone help with this? find st and rt​

Answers

Answer:

ST= 5.2

RT= 23.6

Step-by-step explanation:

Answer:

ST= 5.2

RT= 23.6

Step-by-step explanation:

The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.

Answers

Answer:

A≈1075.21

d Diameter

37

d

r

r

r

d

d

C

A

Using the formulas

A=

π

r

2

d=

2

r

Solving forA

A=

1

4

π

d

2

=

1

4

π

37

2

1075.21009

Step-by-step explanation:

PLZ HELP WILL GIVE BRAINLIEST IF RIGHT!!!

Christian goes out to lunch. The bill, before tax and tip, was $10.40. A sales tax of 6% was added on. Christian tipped 17% on the amount after the sales tax was added. How much tip did he leave? Round to the nearest cent.

Answers

Answer:

$12.89

Step-by-step explanation:

value of tax:

6 : 100 = x : 10.40

x = (10.40 * 6)/100 = $0.624

new amount

10.40 + 0.624 = $11.02

value of tip

17 : 100 = x : 11.02

x = (11.02 * 17)/100 = $1.8734

Final amount

11.02 + 1.8734 = $12.89

A 16-foot ladder is leaning against a wall and the bottom of the ladder is 7 feet from
the bottom of the wall. How high up the wall is the ladder touching?
round to the nearest tenth

Answers

Answer:

13.23 feet^2

Step-by-step explanation:

Uncle Frank has a paddock on his farm. The paddock is a right angled isosceles triangle and has area 16m2. What is the length of fence enclosing the paddock

Answers

Answer:

8 m

Step-by-step explanation:

Applying,

A = bh/2................ Equation 1

Where A = Area of the triangle, b = base of the triangle, h = height of the triangle.

Since the triangle is an isosceles triangle.

Then,  b = h

Assuming, b = y m

Given: A = 16 m²

Substitute these values into equation 1

16 = (y×y)/2

16 = y²/2

y² = 16×2

y² = 32

y = √32

y = 4√2 m

Therefore,

b =  4√2 m and h =  4√2 m

Applying pythagoras theorem, to get the length of the fence enclosing the paddock

a² = b²+c²

a² = (4√2)²+(4√2)²

a² = 32+32

a² = 64

a = √64

a = 8 m

Hence the length of the fence enclosing the paddock is 8 m

4-2(2x-3)-(2x-4)=-2(x+3)

Answers

Answer:

x = 5

Step-by-step explanation:

Given

4 - 2(2x - 3) - (2x - 4) = - 2(x + 3) ← distribute parenthesis on both sides

4 - 4x + 6 - 2x + 4 = - 2x - 6

- 6x + 14 = - 2x - 6 ( add 2x to both sides )

- 4x + 14 = - 6 ( subtract 14 from both sides )

- 4x = - 20 ( divide both sides by - 4 )

x = 5

Answer:

[tex]x = 5[/tex]

Step-by-step explanation:

Let's solve:

[tex]4−2(2x−3)−(2x−4)=−2(x+3) \\ [/tex]

Step 1: Simplify both sides of the equation.

[tex]4−2(2x−3)−(2x−4)=−2(x+3) \\ 4−2(2x−3)+−1(2x−4)=−2(x+3) \\ (Distribute the Negative Sign)

\\ 4+−2(2x−3)+−1(2x)+(−1)(−4)=−2(x+3) \\

4+−2(2x−3)+−2x+4=−2(x+3)

4+(−2)(2x)+(−2)(−3)+−2x+4=(−2)(x)+(−2)(3) \\ (Distribute) \\

4+−4x+6+−2x+4=−2x+−6 \\(−4x+−2x)+(4+6+4)=−2x−6(Combine Like Terms) \\ −6x+14=−2x−6

\\ −6x+14=−2x−6[/tex]

Step 2: Add 2x to both sides.

[tex]−6x+14+2x=−2x−6+2x \\ −4x+14=−6[/tex]

Step 3: Subtract 14 from both sides.

[tex]−4x+14−14=−6−14 \\ −4x=−20[/tex]

Step 4: Divide both sides by -4.

[tex] \frac{ - 4x}{ - 4} = \frac{ - 20}{ - 4} \\ x=5[/tex]

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