Given sin e
; and angle 0 is in Quadrant III, what is the exact value of cos 0 in
simplest form? Simplify all radicals if needed.

Given Sin E; And Angle 0 Is In Quadrant III, What Is The Exact Value Of Cos 0 Insimplest Form? Simplify

Answers

Answer 1

Answer:

[tex]\cos \theta = -\frac{\sqrt{5}}{3}[/tex]

Step-by-step explanation:

Draw a right triangle with angle [tex]\theta[/tex]. In all right triangles, the sine of an angle is equal to its opposite side divide by the hypotenuse of the triangle. Therefore, label the side opposite to [tex]\theta[/tex] as 2 and the hypotenuse (longest side) of the right triangle as 3.

To find the last side, use the Pythagorean Theorem:

[tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle.

Solving for [tex]a[/tex]:

[tex]a^2+2^2=3^2,\\a^2+4=9,\\a^2=5,\\a=\pm\sqrt{5}\implies \sqrt{5}[/tex]

In all right triangles, the cosine of an angle is equal to its adjacent side divided by the hypotenuse. However, the cosine of all angles in Quadrant III are negative. Therefore, the desired answer is [tex]\cos \theta=\boxed{-\frac{\sqrt{5}}{3}}[/tex].

Verify:

[tex]\sin \theta =-\frac{2}{3},\\\\\theta=\arcsin(-\frac{2}{3}}),\\\\\cos(\arcsin(-\frac{2}{3}}))=-\frac{\sqrt{5}}{3}\checkmark[/tex]


Related Questions

Select the correct answer.


Which image shows the correct position of M(-4, 3)?

A.
graph A
B.
graph B
C.
graph C
D.
graph D

Answers

Answer:

Graph A

Step-by-step explanation:

The coordinates for M are x=-4 and y=3

Answer:

Graph A

Step-by-step explanation:

I DID THE TEST AND IT WAS CORRECT :)

find the area of the triangle ABC / acellus

Answers

Answer:

24 squared ft.

Step-by-step explanation:

Area of a triangle is 1/2(b*h)

b=8 ft, c=6 ft

Therefore, area

= 1/2(8*6)

= 1/2(48)

= 24 square ft

(e+8)°
(3e-4°
Need help asap thx

Answers

Answer:

e=44°

Step-by-step explanation:

3e-4+e+8 = 180 degree (being linear pair)

4e+4=180

4e=180-4

4e=176

e=176/4

e=44 degree

If people send links report them

Dan rolls a fair dice and flips a fair coin what is the probability of obtaining an even number and a head

Answers

Half the numbers on the die are even so you have a 1/2 probability of getting an even number. There is also. 1/2 probability of getting heads on a coin flip.

To find the probability of both happening, multiply the probability of each together:

1/2 x 1/2 = 1/4

The probability of getting an even number and heads is 1/4

The answer is 1/4

Dan rolls a fair dice and flips a fair coin what is the probability of obtaining an even number and a head

20
Select the correct pairs of triangles.
The measures of two angles of pairs of triangles are given. Which pairs of triangles are similar?
Triangle 1: 55°, 45°
Triangle 2: 55°, 80°
Triangle 1: 103°, 32
Triangle 2: 103, 25°
Triangle 1: 73°, 47°
Triangle 2: 47°, 30°
Triangle 1: 105°, 23°
Triangle 2: 52°, 105
Triangle 1: 99, 41°
Triangle 2: 40°, 999
Reset
Next

Answers

Answer:

Your answer would be the third one

Step-by-step explanation:

Triangle 1 - 73, 45

Triangle 2 - 47, 30

Triangle 1: 105°, 23° and Triangle 2: 52°, 105 are similar.

Option (4) is correct.

What is a Triangle?

A triangle in geometry is a three-sided polygon with three edges and three vertices.

As per the given data:

We are given two angles for each pair of triangles, and we have to find out which of the pair of triangles are similar.

For any two triangles to be similar, it must have 2 angles which are having the same measure.

For, Triangle 1: 55°, 45° and Triangle 2: 55°, 80°

Only one angle is same, hence not similar.

Triangle 1: 103°, 32° and Triangle 2: 103°, 25°

Only one angle is same, hence not similar.

Triangle 1: 73°, 47° and Triangle 2: 47°, 30°

Only one angle is same, hence not similar.

Triangle 1: 105°, 23° and Triangle 2: 52°, 105

By using angle sum property in Triangle 1 the remaining angles is:

= 180 - (105 + 23) = 52°

By using angle sum property in Triangle 2 the remaining angles is:

= 180 - (52 + 105) = 23°

2 angles are same, hence similar.

Triangle 1: 99, 41° and Triangle 2: 40°, 99°

Only one angle is same, hence not similar.

Hence, Triangle 1: 105°, 23° and Triangle 2: 52°, 105 are similar.

To learn more on Triangle, click:

brainly.com/question/19976619

#SPJ7

How long will it take an investment to triple if the interest is compounded continuously at a rate of
3.75%?
A. 0.3 year
B. 2.93 years
C. 12.72 years
D. 29.30 years
E. 293 years

Answers

D, solved it graphically

what is x+43434343434= 34344

Answers

Answer:

x=−43434309090

Step-by-step explanation:

What is the axis of symmetry for the function f(x)=7−4x+x2?

x = –3
x = –2
x = 2
x = 3

Answers

Answer:

Answer:

x = 2

Step-by-step explanation:

The vertex form of the parabola is given by  

Comparing this equation with vertex form of a parabola , where (h,k) is the vertex

h = 2

k = 3

Hence, vertex is (2,3)

Now, axis of symmetry of a parabola passes through the vertex and divide the parabola in two equal halves.

Hence, axis of symmetry of the parabola is given by

x = h

x = 2

Third option is correct.

Answer:

c

Step-by-step explanation:

HELPPPPPP PLEASEEE!!

Answers

Answer:

the trend is increasing

Step-by-step explanation:

For the figures below, determine the scale factor and the value of x

Answers

Answer:

Scale Factor = 1/2

x = 3

Hope this helps!

Answer:

Step-by-step explanation:

Scale factor = 1/2

x = 6/2 = 3

PLEASE HELP ASAP ITS URGENT

Answers

Step-by-step explanation:

the answer is in the image above

Help please if you don’t mind!!
Thankyou so much

Answers

Answer:

Step-by-step explanation:

[tex]F = \frac{9}{5}C+32[/tex]

Subtract 32 from both sides

[tex]F-32= \frac{9}{5}C\\[/tex]

Multiply both side by 5/9

[tex]\frac{5}{9}(F-32)=( \frac{5}{9})* \frac{9}{5}C\\\\ \frac{5}{9}(F-32)=C\\[/tex]

F= 41

[tex]\frac{5(41-32)}{9}=C\\\\ \frac{5*9}{9}=C\\\\ \frac{45}{9}=C\\\\C = 5\\\\[/tex]

41° F = 5° C

ded the colour of each car going past his house one morning.
e results are shown below.
blue red red silver silver silver silver silver blue silver blue blue black red
red silver silver red black red
complete the table for Jay's results.
Colour
Frequency
blue
red
silver
black
Tally
4 4
= b
till
= 8
2
nich colour of car did Jay record most often?

Answers

Answer:

The correct answer is -

1. An image with correct tally marks and frequency values is attached.

2. Silver

Step-by-step explanation:

The given data of different color cars that going past his house one morning is given in 20 times. The frequency of each car is -

Blue cars - 4 times out of 20

red - 6 times out of 20

silver - 8 times out of 20

black - 2 times out of 20

The complete table is attached as an image -

2. the maximum frequency of the car is the silver car so Jay must have recorded the silver car most often.

Use the algebra tiles to solve the equation 3x -4=11

Answers

I'm sorry I can't answer that but I know something so you can answer that. search in browser or anything searcher "quickmath" or "Cymath" all your problems, equations and more can be solved

Step-by-step explanation:

I hope it helps trust me :-)

Answer: Hi, there your answer is x=5

Step 1: Add 4 to both sides.

3x−4+4=11+4

3x=15

Step 2: Divide both sides by 3.

3x/3=15/3

x=5

Step-by-step explanation:

The straight line 3x + 4y = 24 cuts the y - axis at the point A and cuts the x - axis at the point B. What is the distance AB?​

Answers

Step-by-step explanation:

the answer is in the above image

The distance between point A and point B is 10 units.

What is the distance between two points on a plane?

The distance between two points on a coordinate plane (x, y) and (x, y) is

= √[(x₂ - x₁)² + (y₂ - y₁)²] units

The given straight line is 3x + 4y = 24.

This straight line will cut the x-axis at a point where y = 0.

Therefore, 3x + 4(0) = 24

⇒ 3x = 24

⇒ x = 8

Therefore, the coordinates of the point A is (8, 0).

Similarly, this straight line will cut the y-axis at a point where x = 0.

Therefore, 3(0) + 4y = 24

⇒ 4y = 24

⇒ y = 6

Therefore, the coordinates of the point B is (0, 6).

Therefore, the distance between point A and point B is

= √[(0 - 8)² + (6 - 0)²] units

= √(64 + 36) units

= √100 units

= 10 units   (negative sign is avoided.)

Learn more about the distance between two points here: https://brainly.com/question/12538676

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5) The length of a rectangle is 5 more than 10 times the width. The perimeter is 230cm find the length and width of the rectangle. (I need help please!)

Answers

Answer:

length =105 width =10

Step-by-step explanation:

L=10*W+5

P=230

P=2(L+W)

230=2(10W+5+W)

SOLVE FOR W

W=10

L=10*W+5

=10*10+5

L=105

The Length = 105 width = 10 correct answers to your question

10. Which is the best approximation for Pi? A 14/7 B 44/14 C 14/3 D 3/14​

Answers

Answer:

I think its D 3/14

Step-by-step explanation:

Pi is 3.141592654

If this helps mark as brainllest please!!!

D is the answer ………………………..

Perform the indicated subtraction. -5 - (-6)=

Answers

Answer:

1

Step-by-step explanation:

Answer:

-5 - (-6)= 1

Step-by-step explanation:

hope this is what you're asking for

Area of shaded circle
#17 and #18 with explanations pleaseee​

Answers

ummmmm sorry but good luck

I am less than 20. I am 2 inches more than a foot. Who am I?​

Answers

ANSWER: 14
EXPLANATION:

Match each power of a power expression with its simplified expression

Answers

(4)-

= 4⁰×-⁹

= 4⁰

(-4)²

= -4⁹ײ

= -4¹⁸

=( -4)¹⁸

(4-³)-³

= 4-³ × -³

= 4⁹

(4)-³

= 4⁶ × -³

= 4-¹⁸

= 1/4¹⁸

i’m not sure what the last one is .. can u help pls

Answers

Answer:

136

Step-by-step explanation:

180 - <BAC

Ivy bought 10 packs of cups for her holiday
party. A pack of MEDIUM cups costs $1.80
and a pack of LARGE cups costs $2.40. She
paid a total of $21.60. How many packs of
each size cup did she buy?

Answers

4 packs of medium cups and 6 packs of large cups
Step-by-step explanation:
1.80x + 2.40y = 21.60
1.80(4) + 2.40(6) = 21.60
7.2 + 14.4 = 21.60
21.60 = 21.60

Need quick help with this math

Answers

Answer:

A. 25/33

B. 1/3

C. 1/33

D. 25/9

Answer:

[tex]\text{A. }25/33,\\\text{B. }1/3, \\\text{C. }1/33, \\\text{D. }25/9[/tex]

Step-by-step explanation:

Recall that [tex]\frac{x}{9}=0.\overline{x}[/tex] for [tex]x\in (1, 8)[/tex]. If multiple digits are repeating, increase the number of nines in the denominator as applicable.

Therefore, we have:

Part A:

"75" is repeating:

[tex]\rightarrow \frac{75}{99}=\boxed{\frac{25}{33}}[/tex]

Part B:

"3" is repeating:

[tex]\rightarrow \frac{3}{9}=\boxed{\frac{1}{3}}[/tex]

Part C:

"03" is repeating:

[tex]\rightarrow \frac{03}{99}=\frac{3}{99}=\boxed{\frac{1}{33}}[/tex]

Part D:

"7" is repeating, but there is a terminating decimal 2.0 with it ([tex]2.\overline{7}=2.0+0.\overline{7}[/tex]):

[tex]2+\frac{7}{9}=\frac{18}{9}+\frac{7}{9}=\boxed{\frac{25}{9}}[/tex]

what is an expression showing the sum of 5 less than the number k

Answers

Answer:

 5<k  

Step-by-step explanation:

Answer:

k-5

Step-by-step explanation:

So, lets go over each part of the sentence, and turn it into a expression.

So it first says sum. This means addition, so we can start our expression with:

+

Next is says of 5. So we know its the addition of 5:

+5

Next it says less than. So now we know less than, which is subtraction. So we can swap the addition sign for a - sign:

-5

Finally it says the number k. So we know that the subtracted value is k:

k-5

So this is your expression!

Hope this helps!

find the surface area and volume of the composite

Answers

Answer:

Step-by-step explanation:

To find the surface area of a composite 3D figure, add the areas of each geometric figure making up the composite 3D figure. To find the volume of a composite 3D figure, draw any necessary planes to view the figure as basic three dimensional figures, then: add basic figure volumes belonging to the composite shape.

If valorie made five times more baskets than her brother Vance

But if she made 70 baskets how many baskets did Vance make

Answers

Answer:

I say its 14 because it says  times more" so u would divide 70 by 5 but im debating between 14 and 65

Step-by-step explanation:

okcps.org bookmarks
< BACK TO HOMEPAGE - NORTHWEST CLASSEN NS ALGEBRA I S1 CR 2019-2020
What is the value of
What is the value of g( – 3) when g(x) = 2x – 22
when
Enter your answer in the box.
g(-3) =

Answers

G(-3)= 2(-3)-22=-28

This is the correct answer


What is the coefficient of the expression:
3n+4

Answers

Answer:

The coefficient is 3, the number right before the variable.

Answer:

3

Step-by-step explanation:

(Please help this is due by Tuesday)

Answers

Answer:

A

Step-by-step explanation:

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