Given sinx=1/3, cosy=3/4, and both x and y are in quadrant iv, find cos(x-y) and sin(x+y)

Answers

Answer 1

Answer: [tex]\dfrac{6\sqrt{2}+\sqrt{7}}{12},\ \dfrac{-3-2\sqrt{14}}{12}[/tex]

Step-by-step explanation:

Given

x and y is in the fourth quadrant

[tex]\sin x=-\dfrac{1}{3}\\\\\cos y=\dfrac{3}{4}[/tex]

we know,

[tex]\cos (x-y)=\cos x\cos y+\sin x\sin y\\\sin (x+y)=\sin x\cos y+\cos x\sin y[/tex]

using  [tex]\sin ^2\theta +\cos^2 \theta =1[/tex]

[tex]\Rightarrow \cos x=\dfrac{2\sqrt{2}}{3}\\\\\Rightarrow \sin y=-\dfrac{\sqrt{7}}{4}[/tex]

[tex]\Rightarrow \cos(x-y)=(\dfrac{2\sqrt{2}}{3})\times (\dfrac{3}{4})+(-\dfrac{1}{3})\times (-\dfrac{\sqrt{7}}{4})=\dfrac{6\sqrt{2}+\sqrt{7}}{12}\\\\\\\Rightarrow \sin (x+y)=(-\dfrac{1}{3})\times \dfrac{3}{4}+\dfrac{2\sqrt{2}}{3}\times (\dfrac{-\sqrt{7}}{4})=\dfrac{-3-2\sqrt{14}}{12}[/tex]


Related Questions

A TV has an original price of
$499. Find the new price given a 10% increase

Answers

501 dollars duhhhhhh
change 10% to 0.1
499 x 0.1 = 49.9
499 + 49.9 = 548.9

plz help me with the puiz

Answers

The slope of that line is one!

Barry carefully measured all three sides of the triangle and the dimensions were as follows: 7 meters, 8 meters, 10 meters. Was it a Right Triangle? Please help!

Answers

Answer: Not a right-angled triangle

Step-by-step explanation:

Given

The sides of a triangle are [tex]7\ m, 8\ m, \text{and}\ 10\ m[/tex]

For a right-angle triangle, it must satisfy the Pythagoras theorem

[tex]a^2+b^2=c^2[/tex]

i.e. the square of the larger side must be equal to the sum of the square of the remaining two sides

Here,

[tex]\Rightarrow 7^2+8^2\ ?\ 10^2\\\Rightarrow 49+64\ ?\ 100\\\Rightarrow 113\neq 100[/tex]

Therefore, it is not a right-angle triangle

A forest covers 58,000 acres. A survey finds that 0.7​% of the forest is​ old-growth trees. How many acres of​ old-growth trees are​ there?

Answers

Answer:

406

Step-by-step explanation:

0.7 % / 100 = 0.007

58000 * 0.007 = 406 acres

Can a triangle be formed with the sides lengths of 8 cm, 5 cm and 13 cm?

The side lengths of 8 cm, 5 cm and 13 cm _______ form a triangle.

Drop down options:

cannot
can

Answers

The rule says that the sum of any two sides has to be smaller than the third side so, no it can't

A
Write an explicit formula for an, the nth term of
the sequence 17, 15, 13, ...

Answers

Tn=-2n+19

Step-by-step explanation:

Well in south africa we use Tn

Tn=a+(n-1)d

a=is the first term in the sequence which is 17

d=is the the difference between the terms which is - 2

Tn=17+(n-1)(-2)

Tn=17-2n+2

Tn=-2n+19

How long is side c ? ​

Answers

Answer:

you do pythagorean theorem

Step-by-step explanation:

the base is 8 and the side length is 6 so you do 8²+6²

8²=64 +6²=36

64+36=100 you have to square 100 which is 10

C=10

Which dilation is shown by the graph?

Answers

Answer:

D. D₂ (∆XYZ)

Step-by-step explanation:

Dₙ = (x,y) → ((n)x, (n)y)

_________________

X = (-1, 2).

Y = (2, -1).

Z = (-2, -1).

_________

Dₙ ∆XYZ:

X(-1, 2) → X'(-2, 4)

Y(2, -1) → Y'(4, -2)

Z(-2, -1) → Z'(-4, -2)

______________

-2 / -1 = 2, 4 / 2 = 2.

4 / 2 = 2, -2 / -1 = 2.

-4 / -2 = 2, -2 / -1 = 2.

_______________

D₂ = (x,y) → ((2)x, (2)y).

X(-1, 2) → ((2)(-1), (2)(2)) = X'(-2, 4)

Y(2, -1) → ((2)(2), (2)(-1)) = Y'(4, -2)

Z(-2, -1) → ((2)(-2), (2)(-1)) = Z'(-4, -2)

_________________________

Can anyone help me please ?

Answers

3 I’m not entirely sure though

Write an equation of the line that passes through the points (3,8) and (2.6). Write the equation in slope-intercept form.
The equation of the line in slope-intercept form is

Answers

Answer:

2x - y + 2 = 0 is the equation

y = 2x + 2 is the equation in slope-intercept form

Step-by-step explanation:

slope = (y₂ - y₁) / (x₂ - x₁)

slope = (6 - 8) / (2 - 3)

slope = -2 / -1

slope (m) = 2

equation through the points (3,8) and (2,6):

(y - y₁) / (y₂ - y₁) = (x - x₁) / (x₂ - x₁)

(y - 8) / (6 - 8) = (x - 3) / (2 - 3)

(y - 8) / -2 = (x - 3) / -1

-y + 8 = -2x + 6

2x - y + 2 = 0

slope-intercept form,

y = mx + c

y = 2x + 2

X+3y=17 -2x+3y=-7 how do you solve it

Answers

Answer:

X+3y=17  is  x=−3y+17

-2x+3y=-7  is  x= 3 /2 y+ 7 /2

Step-by-step explanation:

What is the value of this expression? 44−{(6+8)÷2}×3

14

23

69

111

Answers

Answer:

23

Step-by-step explanation:

First, open the brackets.

44 - (14/2) x 3

44 - 7 x 3

44 - 21

23

UHHHH HELP ME PLEASE THANK U

Answers

Answer:

The average or mean of the two fights would be 19.5

Step-by-step explanation:

Basically all you have to do for this problem is add the total scores of the two fights and then divide by 2 to find your mean. 32 plus 7= 39/2= 19.5

find the volume of the solid figure​

Answers

Answer:

Volume= Length × Width × Height

How do you do this what the answer to number 12

Answers

DONT click that link

PLEASE ANSWER URGENT!! TWO QUESTIONS IN ONE
Which number has the least absolute value?
15
5
1
-25

Which number has the greatest absolute value?
15
5
0
-25

Answers

Answer:

1 has the least absolute value and -25 has the greatest absolute value

Step-by-step explanation:

If it is absolute value all numbers will be positive no matter the sign they have

Is it the first one the second one the third one the fourth one ??not to be rude but please hurry !!! 20 points !!!

Answers

Answer:

5/6 ÷ 1/12 = 10

Step-by-step explanation:

5/6 ÷ 1/12     =      5/6 x 12/1 = 60/6 = 10

Proof:

5/6 tank = 10/12 tank

If each trip takes 1/12 tank, then 10 ÷ 1 = 10 trips

if prism A and B have a ratio of similarity of 6:11, what is the volume of prism B if the volume of prism A is 96 cubic units

Answers

Answer:

176cubic units

Step-by-step explanation:

a:b

6:11

a=96

6/11=96/x

6x=1056(96×11)

x=176 cubic units

Determine if the two triangles are congruent. If yes, which theorem proves their congruence?

Answers

Answer:

Not congruent.

The Angle-Side-Side Postulate does not exist because an angle and two sides does not guarantee that two triangles are congruent. If two triangles have two congruent sides and a congruent non included angle, then triangles are NOT NECESSARILLY congruent.

Step-by-step explanation:

HELP ME NOW PLEASE AND THANK YOUUU !! Asap on this questions

Answers

Answer:

y ≥ -1/2x + 1

Step-by-step explanation:

Not the 1st choice since it's going down

Not the 2nd choice since it's solid line

It's the 3rd choice

Answer:

y ≥ -1/2x + 1

Step-by-step explanation:

Hope this helps

Oscar buy his lunch in the school cafeteria the cost of 15 schools lunches is $33.75

Answers

Answer:

$2.25

Step-by-step explanation:

If the answer is how much is one school lunch then...

33.75/15

=2.25

$2.25

It is $2.25 for each meal he gets from school.

3. Write the inverse of the function g(x) =x-3/5

Answers

Answer:(x)= 0.6

Step-by-step explanation:

The graphs below were created by an advertising agency for the computer store TechPlus to show its average price on laptops and desktops compared to another computer store's prices.


Which of the following statements best explains how the advertising agency misrepresented the data?


The graphs use different scales, making it appear that the prices at TechPlus are much lower than CompStar.


The graphs were created with different colors.


The graph for CompStar makes its prices appear much higher, but its prices are only a little higher.


The graphs do not include tablet computers, so there is not enough information to compare their prices.

Answers

The misrepresentation lies in the fact that ; The graphs use different scales, making it appear that the prices at TechPlus are much lower than CompStar.

Taking a look at both graphs, it could be observed on the y - axis that the graphs do not follow the same scale.

For CompStar, the y-axis which shows the price of laptops and desktops starts it's labeling from $0 ; while TechPlus's labeling began from $600

This representation means that comparing the two graphs would give an erroneous inference as it would make the price of TechPlus appear lower than that of Complus.

Learn more : https://brainly.com/question/1370154?referrer=searchResults

easy 25 points!!!!!!!!!

look at the picture provided, find G

Answers

Answer:

There right there u don't see it?

Carly had some markers. After she bought 16 more, she had 40 markers. How
many markers did Carly start with?

Answers

Answer:

24 markers

Step-by-step explanation:

24+16=40

40-16=24

It’s 26. You just do 40 - 16

what is the 30th term In the sequence 10,7,4,1-3,...
determine the term to term rule​

Answers

Answer:

7

Step-by-step explanation:

ok so it 7 but 10 is out so is 3

What is the value of x in the equation shown below?
x3 + 1 = 9

Answers

Answer:

x = 7/3 or 2.33

Step-by-step explanation:

x3 + 1 = 8

x3 = 8 - 1

x3 = 7

x = 7/3 or 2.33

HOPE THIS HELPS YOU!! :)

Answer: x = 2

Step 1.

In order to solve this non-linear equation, we need to move all the terms to the left side.

In x³ + 1 = 9...

- term 1, will be moved to the right side.

Notice that a term changes sign when it 'moves' from one side of the equation to the other.

Rewrite the equation like this:  (x³ + 1) + (-1) = 9 + (-1)

Step 2.

Add x³ + 1 + (-1)

x³ + 1 + (-1) = 8

Now, x = 8.

Step 3.

In this non-linear equation, the variable needs to be isolated.

This is accomplished when both sides are exponentiated by the reciprocal of the variable's exponent, which in our example, 1/3 is equal to

Notice that since we exponentiated a simplified fraction with an odd denominator, only one solution has been created.

Rewrite the equation: [tex](x^3)^\frac{1}{3} =8^\frac{1}{3}[/tex]

Step 4.

We need to exponentiate the power.

The following rule is applied: [tex](A^B)^C=A^B^C[/tex]

According to the formula,

A = X

B = 3

C = 1/3

Rewrite the equation: [tex]x^3^\times^\frac{1}{3} =(2^3)^\frac{1}{3}[/tex]

Step 5.

We need to reduce this fraction, the 3 in x to the lowest terms.

This can be done by dividing out those factors that appear both in the numerator and in the denominator.

In our example, 3 is the common factor.

Rewrite the equation: [tex]x=2^\frac{3}{3}[/tex]

Step 6.

Lastly, we'll need to do the same thing as we did in step 5. Reduce the fraction in [tex]x=2\frac{3}{3}[/tex]. This can be done by dividing out those factors that appear both in the numerator and in the denominator.

Hence, the common factor is 3 since it occurs both in the numerator and the denominator.

Hence, x = 2.

#1) Catherine takes AC transits to school and the bus travels 35 blocks in 7 minutes. At this rate, how long
should the ride take if Catherine's school is 50 blocks away from her house? Explain how you know.

Answers

10 minutes, you divide the blocks (35) by the time (7) which will give you the amount of blocks per minute which is 5 and you divide the amount you live (50) and you get 10 minutes

find the solution of given expression

[tex] \sqrt{652 \times 652} [/tex]

Answers

Answer:

652

Step-by-step explanation:

[tex]\sqrt{652 \times 652}[/tex] is equal to [tex]\sqrt{652^{2} }[/tex], and the square root of a number squared is always the original number, so [tex]\sqrt{652^{2} }[/tex] is equal to [tex]652[/tex].

Answer:

√{652×652}=√652²=±652

Step-by-step explanation:

Solve the equation for x, and enter your answer in the box below.
x + (-12) = 11
Answer here

Answers

x+(-12)=11
+12 +12
x =23

Answer:

X=23

Step-by-step explanation:

x + (-12) = 11

Open the bracket

x-12=11

Collect like terms

X=11+12

X=23

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