If tanΘ = 6/5 and cosΘ < 0, what is sin2Θ?
An explanation on how to solve this problem would be great, thanks!!

Answers

Answer 1

Answer:

[tex]\displaystyle \sin2\theta=\frac{60}{61}[/tex]

Step-by-step explanation:

We are given that:

[tex]\displaystyle \tan\theta=\frac{6}{5}\text{ and } \cos\theta <0[/tex]

And we want to find the value of sin(2θ).

First, recall that tangent is the ratio of the opposite side to the adjacent side.

Therefore, the hypotenuse is:

[tex]h=\sqrt{6^2+5^2}=\sqrt{61}[/tex]

Next, note that tangent is positive and cosine is negative. Tangent is positive in QI and QIII. Cosine is negative in QII and QIII.

Hence, we can conclude that θ must be in QIII.

In QIII, sine is negative, cosine is negative, and tangent is positive.

And with respect to θ, our opposite side is 6, adjacent side is 5, and the hypotenuse is √(61).

We can rewrite our expression as:

[tex]\sin2\theta=2\sin\theta\cos\theta[/tex]

Using the above information, substitute:

[tex]\displaystyle =2\left(-\frac{6}{\sqrt{61}}\right)\left(-\frac{5}{\sqrt{61}}\right)[/tex]

Simplify. Hence:

[tex]\displaystyle \sin2\theta=\frac{60}{61}[/tex]


Related Questions

PLEASE HELP ME I WILL HIVE BRAINLYEST

Answers

Answer:

Step-by-step explanation:

a). Points on a number line are,

    x = -7, 1

    Number of small blocks between x = -7 and 1 is 8.

    Distance = 8

b). Difference between two points x = -7, 1 will be,

    1 - (-7) = 1 + 7

               = 8

    -7 - 1 = -8

c). Absolute value of each difference,

    |1 - (-7)| = 1 + 7

                = 8

    |-7 - 1| = |-8|

              = 8

How do you find the area of a circle???

Answers

The area of a circle is pi times the radius squared
A= π r2 Depending on what the value is in “r”

plss help me!!

Find the length of the arc.

Answers

Answer:

[tex]\frac{5\pi }{2}\:ft[/tex] (Option D)

Step-by-step explanation:

GIVEN :-

Angle subtended by the arc at center (θ) = 90°Radius of the circle = 5 ft.

TO FIND :-

Length of the arc

GENERAL FORMULAE TO BE USED IN THIS QUESTION :-

Lets say an arc subtends ∠θ at the center of the circle whose radius is 'r'.

[tex]=> Length \; of \; the \; arc = \theta \times \frac{\pi r}{180}[/tex]

SOLUTION :-

Length of the arc = [tex]\theta \times \frac{\pi r}{180} = 90 \times \frac{5\pi }{180} =\frac{5\pi }{2}[/tex]

Determine if the two triangles in the image above are similar. If so, what’s the correct postulate. SSS, SAS, AA, or None

Answers

Answer:

SAS

Step-by-step explanation:

What number has a value less than 14.7?​

Answers

Answer:

Anything below 14.7

Step-by-step explanation:

PLEASE HELP QUICK ITS TIMED



Dawson has 3 more tokens than twice the number of tokens that Rachel has. Dawson has
21 tokens. What is the total number of tokens Rachel has?

Answers

Answer:

9

Step-by-step explanation:

I think what they are asking is to subtract the 3 tokens from 21 tokens he already has giving us 18. and since it says "Twice the number of tokens" I'm assuming you divide 2 from 18 giving you 9 tokens.

Answer:

9 divided by 21

Step-by-step explanation:

17

Given the conversion factor 12/1 in over 1ft, which cube has the larger surface area?

Answers

Answer:

Solid A

Step-by-step explanation:

3 feet is 3 x 12 = 36 inches, which is less than 48 inches, so solid A has a larger surface area than solid B.

NO LINKS PLEASE ..Solve for x

Answers

Answer:

x = 42.5

Step-by-step explanation:

all triangles inscribed into a circle like in the picture must have a 90 degree angle.

so, 90 = 2x + 5, 85 = 2x, x = 85/2 = 42.5

If a movie begins at 5:10 p.m. and runs for 1 hour and 45 minutes, what time will the movie end?

(Answer:_:__p.m.)​

Answers

Answer:

6:55 p.m

Step-by-step explanation:

Hour connects with hour therefore, 5 + 1 = 6

Minutes connects with minutes thus, 10 + 45 = 55

Hence it being 6:55 p.m when the movie finishes if it starts at 5:10 p.m.

What type of graph is best to use to show data that are parts of a whole?

Answers

Answer:

Pie charts

Step-by-step explanation:

A Pie Chart. Pie charts are best to use when you are trying to compare parts of a whole.

Answer:a Pie Chart. Pie charts are best to use when you are trying to compare parts of a whole.

Step-by-step explanation:a Pie Chart. Pie charts are best to use when you are trying to compare parts of a whole.

Jensen goes to the store with $4. He buys 3 pencils for $0.70 each and
some erasers. Each eraser costs $0.50. Enter the maximum number of
erasers he can buy.

Answers

Answer:

3 erasers.

Step-by-step explanation:

Let p = pencils and e = erasers. Since we know that Jensen has $4, we can set up the following inequality and solve for e.

0.70p + 0.50e ≤ 4

0.70(3) + 0.50e ≤ 4

2.10 + 0.50e ≤ 4

0.50e ≤ 1.90

e ≤ 3.8

Since erasers are usually bought as whole items, the maximum amount of erasers Jensen can buy is 3.

If P = (-1,6), Find: Rx-axis (P).

Can you show me how to do this?
And explain lt to me like I'm 8 xD
appreciate it.
I hate math lol.

Answers

Answer:

Step-by-step explanation:

its (-1,-6)

this is your answer

Question 16 of 20
To the nearest hundredth, what is the circumference of a circle with a radius
of 7 units?
A. 43.98 units
B. 21.99 units
C. 35.75 units
D. 153.94 units

Answers

Answer:

43.98

Step-by-step explanation:

The circumference of a circle with a radius of 7 units is approximately 43.98 units, which corresponds to option A.

What is the Circumference of a circle?

The Circumference of a circle is defined as the product of the diameter of the circle and pi.

Given that the radius of the circle is 7 units, we can substitute this value into the formula:

To find the circumference of a circle, we can use the formula C = 2πr, where C represents the circumference and r represents the radius.

C = 2π(7) = 14π

Use the approximation π ≈ 3.14:

C ≈ 14(3.14) = 43.96

Rounding this value to the nearest hundredth, we get approximately 43.98 units.

Therefore, the circumference of a circle with a radius of 7 units is approximately 43.98 units.

Learn more about the Circumference of the circle here:

brainly.com/question/19794723

#SPJ7

I need to get an a please help

Answers

Answer:

n ≥ -5/14

Step-by-step explanation:

64n - 6 ≥ 36n -16

subtract 36n from each side

64n -36n - 6 ≥ 36n-36n -16

28n - 6 ≥  -16

add 6 to each side

28n -6+6 ≥  -16+6

28n ≥ -10

Divide each side by 28

28n/28 ≥ -10/28

n ≥ -5/14

Answer:

n ≥ -5/14

Step-by-step explanation:

64n - 6 ≥ 36n -16

subtract 36n from each side

64n -36n - 6 ≥ 36n-36n -16

28n - 6 ≥  -16

add 6 to each side

28n -6+6 ≥  -16+6

28n ≥ -10

Divide each side by 28

28n/28 ≥ -10/28

n ≥ -5/14

Find missing measure (No.6)

Answers

Answer:

Step-by-step explanation:

6 no

1.angle 2=92 degree(being vertically opposite angle)

2.angle 1+33+92=180(sum of interior angles of a triangle)

angle 1+125=180

angle 1=180-125

angle 1=55

3.angle 3+angle 2+115+90=360(sum of four angles is always 360 degree)

angle 3+92+205=360

angle 3+297=360

angle 3=360-297

angle 3=63

Help I'm gonna fail
A pet store owner had her staff count the number of fish in each tank. Which interval has the fewest tanks?

Answers

Its would be 41-60 I’m pretty sure
it is 41-60

explanation:

Thank for doing l love u

Answers

i think the answer for the first 2 questions are 12 and 28

good job guys ik math is hard sometimes

The height of a refrigerator would be about?
A. 7 inches
B. 7 feet
C. 7 yards
D. 7 miles​

Answers

The correct answer is B. 7 feet

Answer:

i think its b) 7 feet

Step-by-step explanation:

A ship from Port travels fot 60km on the bearing of 129°.It continues to travel and changes direction for another 50km on a bearing of 080°

Answers

Answer:

The ship is approximately 100 km to the Port.

Step-by-step explanation:

The sketch to the question gives a triangle with two sides and an included angle. Let the distance from the Port to the stopping point of the ship be represented by c. It can be determined by the application of cosine rule. Cosine rule states that:

[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] -2ab Cos C

a = 50 km

b = 60 km

C = 51 + 80 = [tex]131^{o}[/tex]

So that;

[tex]c^{2}[/tex] = [tex]50^{2}[/tex] + [tex]60^{2}[/tex] -2(50 x 60) Cos [tex]131^{o}[/tex]

   = 2500 + 3600 -6000 x -0.6561

   =  6100 + 3936.6

[tex]c^{2}[/tex] = 10036.6

c = [tex]\sqrt{10036.6}[/tex]

  = 100.183

c = 100.18 km

Thus, the ship is approximately 100 km to the Port.

PLEASE HELPPP, ITS DUE IN 1 HOUR!! I WILL GIVE BRAINLIEST!! LINKS=REPORT
PLEASE SOLVE FOR THE CHART AND GRAPH. PLEASE SHOW ON GRAPH

Answers

Answer:

3=6

4=8

5=10

6=12

graph 1

Step-by-step explanation:

Find the slope of the graph below. Help fast

Answers

Answer:

2x

Step-by-step explanation:

(5,5) is a point (I reckon it is from the screenshot you sent at least)

(0,-5) is a point

-5 - 5 = -10

0 - 5 = -5

-10/-5

Slope = 2x

Answer:

Two Possible Points:

5,5 and 6,7

7 - 5         2

____ = _____ = your slope is 2

6 - 5          1

When picking two points subtract the y(rise) from eachother first which will be your numerator and the x(run) from eachother in the same exact way you subtracted to the y which will be your denominator.

Mr. Roundtree had 20 tickets. He gave 10 to his family and 8 to his friends.​

Answers

He has two tickets left

the only solution to x² + bx + c = 0
is x = 5

work out the values of b and c​

Answers

Answers:

b = -10

c = 25

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

Explanation:

If x = 5 is the only solution then (x-5) is the only factor. Turns out we have repeated solutions and repeated factors. Meaning (x-5)(x-5) = (x-5)^2 is what we're after.

Expand that out to get

(x-5)^2

x^2 - 5x - 5x + 25

x^2 - 10x + 25

Then compare this to x^2 + bx + c to find

b = -10

c = 25

If you were to solve x^2-10x+25 = 0, you'll find that x = 5 is the only root.

Pls help I’ll give brainlest

Answers

the answer is 40 yards. hfjjfnfhcnfnc

The value of a house has increased by 5% the house is now valued at £609000 what is the value of the house before the increase? I found a post that answered the question but it didn't explain how they got the answer.

Answers

Answer:

[tex]Current \ price = 609000\\\\Let \ the \ original \ price \ be = x\\\\\% increase = 5 \% \ of \ x = \frac{5}{100} \times x = \frac{5x}{100}\\\\Price \ after \ increase, current\ price = \frac{5x}{100} + x\\\\[/tex]

[tex]=> 609000 = \frac{5x}{100} + x\\\\=>609000 = \frac{105x}{100}\\\\=> x = \frac{609000 \times 100}{105}\\\\x = 580000[/tex]

Therefore original price = $580,000

What is the least common multiple of the two denominators 6/8 and 4/32, only answer are 18, 8, 32, and 12 which one there are no 4

Answers

Answer:

32

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

the correct answer is 32

how many puppies were rescued 12x+3=

Answers

Answer:

36

Step-by-step explanation:

12 x 3 = 36

What is that number in scientific notation form??

Answers

Answer:

D. 3.7 × 10⁶

Step-by-step explanation:

3.7 × 10⁶

3700000

MATH PLEASE HELP ! PLEASE

Answers

Answer:

wait I am solving this

Step-by-step explanation:

mark it as the brainliest to get the answer

A DrillingRick was diggingA well in the valley it dug to a point of -50 Meters in one day After 18 hours at how many meters would the rig be if it moved at the same amount each hour? Show your work.Explain your answer

Answers

Answer:

37.5 meters

Step-by-step explanation:

depth of well : hours of digging

it dug to a point of -50 Meters in one day

= 50 meters : 24 hours

After 18 hours at how many meters would the rig

Let

x = depth that will be rigged

depth of well : hours of digging

= x meters : 18 hours

Equate the ratios

50 meters : 24 hours = x meters : 18 hours

50/24 = x/18

50 * 18 = 24 * x

900 = 24x

x = 900/24

x = 37.5

x = depth that will be rigged = 37.5 meters

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