Given: cos θ=-4/5, sin x = -12/13, θ is in the third quadrant, 
x is in the fourth quadrant; evaluate 
tan2θ
A. 24/5
B. 24/7
C.12/13

Given: Cos =-4/5, Sin X = -12/13, Is In The Third Quadrant, X Is In The Fourth Quadrant; Evaluate Tan2A.

Answers

Answer 1

By definition of tangent,

tan(2θ) = sin(2θ) / cos(2θ)

Recall the double angle identities:

sin(2θ) = 2 sin(θ) cos(θ)

cos(2θ) = cos²(θ) - sin²(θ) = 2 cos²(θ) - 1

where the latter equality follows from the Pythagorean identity, cos²(θ) + sin²(θ) = 1. From this identity we can solve for the unknown value of sin(θ):

sin(θ) = ± √(1 - cos²(θ))

and the sign of sin(θ) is determined by the quadrant in which the angle terminates.

We're given that θ belongs to the third quadrant, for which both sin(θ) and cos(θ) are negative. So if cos(θ) = -4/5, we get

sin(θ) = - √(1 - (-4/5)²) = -3/5

Then

tan(2θ) = sin(2θ) / cos(2θ)

tan(2θ) = (2 sin(θ) cos(θ)) / (2 cos²(θ) - 1)

tan(2θ) = (2 (-3/5) (-4/5)) / (2 (-4/5)² - 1)

tan(2θ) = 24/7


Related Questions

Justin and Dan ordered a pizza. Justin ate 1/4 and ate 3/8 of the pizza what fraction of the pizza is left? please show how you got the answer.

Answers

Answer:

3/8 of the pizza is left

Step-by-step explanation:

say the pizza was cut into 8 slices. Justin at 1/4 of the pizza, we can also put that as 2/8. so now 2 slices are gone. that leaves us with 6 slices. Dan ate 3/8 so now 3 more slices are gone. now we only have 3 left. since we started out with 8 we'll use that as a denominator; 3/8. or look at the image attached

Answer:3/8

Step-by-step explanation:

HELP ME PLZ!!!!! ..................................

Answers

Step-by-step explanation:

the the number on the top corner is adding zeros so 6.3 / 10/3 the answer is for that 6.30

1. 90.4
2. 904
3. 9040
4. 90400
5. 904000


If cos 67° is close to 25, which is closest to the length of NO?
Options
2 centimeters
20 centimeters
40 centimeters
60 centimeters

Answers

60 centimeters your welcome

Which lines have a y-intercept at (0,4)?
Choose all answers that apply:
А
y=-3x +4
B
y = 4x + 7
y = 5 + 4x
y = 4-2

KHAN ACADEMY

Answers

Answer:

y=-3x+4

Step-by-step explanation:

Using the formula y=mx+b

mx= slope b= y-intercept

hence,

y=-3x+4 has a y-intercept of (0,4)

Answer:

A y=3x +4

Step-by-step explanation:

since when x=0 then y will be at +4

Y=3(0)+

PLEASE HELP ASAP!!!
A group of students must collect at least $120 to organize a science fair. They have already collected $30. Which graph best represents all remaining amounts of money, in dollars, that the students should still collect to organize the science fair? Number line graph with closed circle on 120 and shading to the right Number line graph with closed circle on 90 and shading to the right. Number line graph with closed circle on 150 and shading to the right Number line graph with closed circle on 30 and shading to the right.

Answers

Answer:

OPITON 2

Step-by-step explanation:

120-30=90 SHE NEED 90 DOLARS MORE

HEEEEEEEEEEEEEELLLLLLLLLLLLLLLLLLPPPPPPPPPPPPPPPPPP

Answers

Answer:

x = 12

Step-by-step explanation:

Given:

m<BCF = 4x°

m<CFE = 11x°

Required:

m<BCF and m<CFE

SOLUTION:

m<BCF + m<CFE = 180° (same side interior angles are supplementary)

Substitute

4x + 11x = 180

15x = 180

Divide both sides ny 15

15x/15 = 180/15

x = 12

what is 27+27 BumblebeeTuna

Answers

your answer is 27+27 = 54

Answer: 54

Step-by-step explanation:

State the domain and range of f(x)=[[x-2]]

Answers

Answer:

domain: -infinity < x <infinity or (-infinity, infinity)

range: -infinity < f(x) < infinity or (-infinity, infinity)

Step-by-step explanation:

Solve the system of equations.
2r+3s=-5
3r+5s=-9
Type an ordered pair​​

Answers

Answer:

2r + 3s= 9 <=> -6r -9s = -27;

3r + 2s= 12 <=> 6r + 4s = 24;

                   => 0*r -5*s = -3 => s = 3/5;

2*r + 3*(3/5) = 9<=> 10*r + 9 = 45 <=> 10*r = 36 => r = 18/5;

PLEASE HELP thank u very much
Martina designed a painting for art class, as shown in the drawing below. Her design contains 4 circles on a square canvas. Each circle has a radius of 6 inches. The circles touch the edges of the canvas and each other, as show below.
The shaded section of Martina's design will be painted black. Which is closest to the area that will be painted black?​

Answers

Answer:

area of shaded region =(6×4)²-4(π6²)=123.61in²

Answer:

area of shaded region (6x4)²-4(6²)=123.61in²

s

I have 6 congruent faces and 2 bases.

Answers

Answer:

A cube

Step-by-step explanation:

A cube has 6 of the same faces and there are 2 bases

a cube, a cube has 6 congruent faces and 2 bases

PLSSS HELP AND GIVE THE RIGHT ANSWER!!!!!!!!!!!!!!!!!!!
The fourth graders are having lunch in the schoolyard. Two classes of 30 students each, 2 teachers and 2 parents will be there. If 8 people sit at each table, how many tables will be needed for all the people having lunch in the schoolyard?
a) 8
b) 60
c) 64
d) 9

Answers

Answer:

8 tables

Step-by-step explanation:

2 class * 30 students + 2 teachers + 2 parents

= 64 people

64 people * 1 table/8 people = 8 tables

Mark brainliest if this helped

Mark brainliest if this helped

Step-by-step explanation:

8 tables because 30+30 =60

and 2+2=4 which is 64 and 8×8=64

Find the mean absolute deviation of the set of data. Round your answer to two
decimal places.
78, 45, 60, 33, 84

Answers

Here is a photo of the decimal places

PLEASE HELP SMART PEOPLE :C

Answers

Answer:

C 290 in^2

Step-by-step explanation:

you need 4/5 of a cup of strawberries for a single pie, how ,many cups are need for 9 pies?

Answers

Answer:

7 2/5 cups

Step-by-step explanation:

4 x 9 = 36

36/5 = 7.2

The Reeds are moving across the country. Mr. Reed leaves 4.5 hours before Mrs. Reed. If he averages 40mph and she averages 60mph, how many hours will it take Mrs. Reed to catch up to Mr. Reed?

Answers

Mr. Reed DATA:

rate = 40 mph ; time = x 4.5 hrs ; distance = 40x miles

-----

Mrs. Reed DATA:

rate = 60 mph ; time = x hrs ; distance = 60x - 210 miles

------

Equation:

40x = 60x -210

-20x = -210

x = 10.5 hrs

x-3.5 = 7 hrs (Mr. Reed's time)

Please help.
You will get brainliest.

Answers

Answer:

[tex] 18,432\pi \: {in}^{3} [/tex]

Step-by-step explanation:

Base diameter of cylinder = 48 in

So, base radius (r) = 48/2 = 24 in

Height of oil filled in the can (h) = 32 in

Volume of portion of the can that is filled with oil

[tex] = \pi {r}^{2} h \\ \\ = \pi \times (24)^{2} (32) \\ \\ =18,432\pi \: {in}^{3} [/tex]

I really need help I would appreciate it if someone could help me

Answers

Answer:

a) The vertex of the graph is [tex](h,k) = (0, 31)[/tex], b) [tex]a = -16[/tex], c) The equation of the parabola is [tex]f(t) = -16\cdot t^{2}+31[/tex].

Step-by-step explanation:

a) The tennis ball experiments a free fall, that is, an uniform accelerated motion due to gravity and in which effects from Earth's rotation and air viscocity are negligible. The height of the ball in time is represented by a second order polynomial. Hence, the vertex of the parabola is the initial point highlighted in graph.

The vertex of the graph is [tex](h,k) = (0, 31)[/tex].

b) If we know that [tex](h,k) = (0, 31)[/tex], [tex]f(t) = a\cdot (t-h)^{2} + k[/tex] and [tex](t,f(t)) = (1,15)[/tex], then the value of [tex]a[/tex] is:

[tex]f(t) = a\cdot (t-h)^{2} + k[/tex]

[tex]15 = a\cdot (1-0)^{2}+31[/tex]

[tex]15 = a\cdot 1 + 31[/tex]

[tex]a = 15-31[/tex]

[tex]a = -16[/tex]

c) The equation of the parabola is [tex]f(t) = -16\cdot t^{2}+31[/tex].

Constance has an apple that weighs 85,000 milligrams and a peach that weighs 0.15 kilograms. Which fruit has the greater mass? Choose the words and numbers to complete the statements. Convert the masses of both fruits to the same unit.

Answers

Answer:

The peach will way more then the apple

Hope this helps you ☜(゚ヮ゚☜)

The weight of the peach is greater than the weight of apple

What is unit conversion?

In order to translate measurements of a particular amount between different units, a mathematical conversion factor is usually used. This modifies the measurement of the quantity without altering its effects.

The particular circumstances or the intended result control the conversion process. This may be governed by law, a contract, a list of technical specifications, or other publicly available standards.

A precise conversion from one system to another is necessary for some measures in order to maintain the precision of both the original measurement and the conversion.

Based on the connection between a particular pair of original units and a particular pair of target units, each conversion factor is chosen.

Given data ,

Let the weight of apple be = 85,000 milligrams

And , let the weight of the peach be = 0.15 grams

Now , from the unit conversion

1 gram = 1000 milligrams

And , 1 kilogram = 1000 grams

So , the weight of apple A = 85 grams

And , the weight of the peach P = 150 grams

Therefore , P > A

Hence , weight of peach is larger

To learn more about unit conversion click :

https://brainly.com/question/19420601

#SPJ3

find the 12th term in the sequence: 1/16, -1/8, 1/4

Answers

Answer:

Step-by-step explanation:

hello :

the sequence is geometric because : (1/4)/(-1/8) = (-1/8)/(1/16)=-2   = r

the nth term is :  An =A1 × r^(n-1)

a common ratio is : r  and A1 the first term

in this exercice :   r =2         A1 = 1/16

when : n =12 you have the  12rd term  A12

A12 = 1/16 × 2^(12-1)  = 1/16 × 2^(11)

Elevii au studiat o schiță a corpului uman. Ei au observat că ar putea trasa pe schiță un
cerc pentru care centrul O și punctele A , B și C sunt corespunzătoare unor structuri
anatomice.
Cercul este reprezentat în figura alăturată. Centrul
cercului este punctul O, BC este diametru al cercului, iar
punctul A este situat pe cerc, astfel încât ∢BAO = 60° . Raza
cercului este de 2cm .

6. Calculează lungimea diametrului BC .

7. Determină măsura arcului mic AC .

Answers

Answer:

an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

Which of the following verbal sentences represents the algebraic sentence below?
2x – 5 = -15

Answers

five subtracted from two x is equivalent to negative 15

Calculate the perimeter of the above triangle.
10 units
30 units
5:
22.9 units
17.1 units

Answers

Step-by-step explanation:

1.

The obvious question to ask in this situation is, “how many miles does Joseph travel on Mondays”? To compute, we each distance: 3 + 6 + 6 = 15.

Joseph travels 15 miles on Mondays.

3.Perimeter means “distance around a closed figure or shape” and to compute we add each length: 3 + 6 + 6 = 15

4.Solution

Just keep adding those side lengths. 6 + 7 + 4 + 4 + 5 + 6 + 2 = 34 units

If you look closely at the shapes in the previous examples, you might notice some ways to write each perimeter as a more explicit formula. See if the results from what we have done so far match the formulas below.

i will give brainliest if you answer this simple question.
if you have 5 candy bars in a bowl and take out 3 how many do you have now?

Answers

Answer:

2

Step-by-step explanation:

5-3=2 you subtract to get the answer

Answer:

2 in the bowl and 3 in the hand

Step-by-step explanation:

The final answer could be anywhere between 2 and 5 depending on what you did with the candy once it was taken out of the bowl. But, the most obvious answer would be 2 left and 3 technicallly gone

A repair engineer charges a customer £50 for every job and £25
for every hour that he works. Which formula could you use to
find how much he charges, C, for h hours of work?

Answers

I don’t know if there were options to choose from, but if I had to make a formula it would be: 50 + 25h = C

girl name are April, may, June, what is the name the mother?​

Answers

mary is the 4th childs nam,e

find the missing side of each triangle using the pythagorean theorem

Answers

Answer:

x=5

Step-by-step explanation:

The pythagorean theorem stats a^2+b^2=c^2. We are already given the values of the two legs of the triangle so we need to solve for the length of the hypotenuse (the longest part of the triangle). To do so, you put in 3 and 4 as a and b so you get 3^2+4^2=c^2. After squaring both numbers you get 16+9=c^2. Then you add 16 and 9 to get 25=c^2. To get rid of the power of 2, we square root both sides to get rid of the exponent. Since 25 is a perfect square, you get c=5 which means that the x value eqals 5.

5+5(6*7)Easy points cause I love y’all pur

Answers

tysmmm ilyyyyyyyyyyyyyyyy

Evaluate f(x)=−5ex+4+3 for x=−6.

Answers

Answer:

f(-6) = 30e+7 or 88.55

Step-by-step explanation:

First you want to plug in the -6 into the function getting you:

-5e(-6)+4+3

You can multiply the -5*-6=30

Then add 4+3 giving you 7

So the final answer is 30e+7

PLEASE HELP ME ON THIS!

the height of a rectangular prism is 8 meters, and the volume is 308 cubic meters. what is the area of the prisms base in square meters?

Answers

9514 1404 393

Answer:

  38.5 square meters

Step-by-step explanation:

The relevant volume formula is ...

  V = Bh . . . . where B is the area of the base, and h is the height

Solving for B, we get ...

  B = V/h

  B = (308 m³)/(8 m) = 38.5 m²

The area of the prism's base is 38.5 square meters.

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