The terminal side of θ in standard position contains the point (–4, 3). Find the exact values of the six trigonometric functions of θ. (show all of your work) *

Answers

Answer 1

Answer:

When we have a rectangular point (x, y), the angle between the x-axis and a ray that connects the origin with this point is given by:

Tan(θ) = y/x.

Cos(θ) = x/(√(x^2 + y^2))

Sin(θ) = y/(√(x^2 + y^2))

So for the point (-4,3) we have:

x = -4

y = 3

√( (-4)^2 + 3^2) = √(16 + 9) = √25 = 5

Then:

Tan(θ) = 3/-4 = -(3/4)

Sin(θ) = 3/5

Cos(θ) = -4/5

And for the other 3 trigonometric functions (the inverses of the 3 above ones) we have:

Ctg(θ) = 1/Tan(θ) = -4/3

Csc(θ) = 1/Sin(θ) = 5/3

Sec(θ) = 1/Cos(θ) = -4/5


Related Questions

hello there. can you help with this. thank you :D

you get 20 points ^^

Answers

Answer:

A - 3

B - 5

C - 1

D - 2

E - 6

F - 4

Sorry too tired to explain ;-;

But hope this helped, and yes, it is for sure correct!

(pls consider brainliest? :D)

A certain television is advertised as a 54-inch TV (the diagonal length). If the width of the TV is 40 inches, how tall is the TV? Round to the nearest tenth of an inch.

Answers

Answer:

36.3

Step-by-step explanation:

I tried using the Pythagorean Theorem to measure the length (tallness) of the TV.

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

[tex]a^2 + (40)^2 = (54)^2[/tex]

[tex]a^2 + 1600 = 2916[/tex]

[tex]a^2 = 2916-1600 = 1316[/tex]

[tex]a = \sqrt{1316}[/tex]

[tex]a = 36.27671429[/tex]

When this is rounded up to the nearest tenth, it would go up to 36.3.

So, the length (tallness) of the TV would be 36.3 inches.

a boy kicks a 0.445kg soccer ball with the force of 75 newtons what is the acceleration of the soccer ball

Answers

Answer:

168.5 m/s^2

Step-by-step explanation:

The perimeter of a square is 100. The side length is represented by 2x+3. Solve for x.

Answers

Answer:

4×side length=perimeter of the square

4×(2x+3) = 100

2x+3 = 25

2x=25-3=22

x=11

At the aquarium, posters of sharks cost $2 and posters of jellyfish cost $6. Mr. Benson spent $64 to buy 12 posters. How many of each type of poster did Mr. Benson buy?

Answers

Answer:

8

Step-by-step explanation:

Step 1: Add the cost of the posters together

Shark: 1 = $2

Jellyfish: 1 = $6

2 + 6 = 8

Step 2: Divide the result by the total amount Mr. Benson spent

64 ÷ 8

[tex]= \frac{64}{8}[/tex]

[tex]= 8[/tex]

Therefore, Mr. Benson bought 8 of each type of poster.

3 cm 15 cm 18 cm What volume of nuts could the container hold? a 270 cm b 869 cm c 738 cm d810 cm​

Answers

Answer:

d-810 cm

Step-by-step explanation:

mutiply

3x15x18=810

Please help! Struggling with this a bit

Answers

Answer:

Rate of change= 9   Starting amount= 65

The equation would be y= 9x + 65

After 9 months, he would have 146 vreels

For the graph, put the points (0, 65) (2, 83) and (4, 101)

help meeeeeeeeeeeeeeee. this is due tomorrow

Answers

Answer:

common difference increases by 2 times

d = (2×12) = 24

[tex] {a}^{4} + {b}^{4} + {c}^{4} = (22 + (12 \times 2)) \\ = 46[/tex]

Find the ratio in simplest form.

a) 24 to 56​

Answers

i’ll show you step by step
24:56
12:28
6:14
3:7

how do you factor this trinomial? 2x² + 9x - 18

Answers

Factor by grouping.

(2x + 3)(x − 6)

Answer:

(2x-3) (x+6)

Hope this helps :)

Equations on both sides
3x + 5 = 2x -17

Solve it and show the work because i need to show the work

Answers

The answer would be for this problem is -22

Answer:

x = -22

Step-by-step explanation:

Subtract 5 from both sides

3x + 5 (-5) = 2x - 17 (-5)  

3x = 2x - 17

Subtract 2x from both sides

3x (-2x) = 2x (-2) -22  

x = -22

How wide is the pond?

Answers

20ft

Step-by-step explanation:

lil kitty on the roof all aloe without his lady

A rectangle prism has a base with an area of 20 square centimeters and a height of 3 centimeters. What is the volume of the prism?

Answers

Answer:

Step-by-step explanation:

The volume of a rectangular prism is shown below:

We are given the an area of  

173.6

 

cm

and a height of  

9

 

cm

.

We also know that the formula for area is  

l

w

, meaning we can substitute the area for  

l

w

in the volume formula.

Now let's plug in what we know into the formula and solve for the volume:

V

=

(

173.6 cm

2

)

(

9 cm

)

 

 

=1562.4 cm

3

The volume of the rectangular prism is  

1562.4 cm

3

.

The point (3, -1) is on the line given by which equation below?


A. y = -3x
B. y = x - 4
C. y = x + 4
D. y = 3x

Answers

Answer:

Just grabbin points

Step-by-step explanation:

Answer:

B. y = x - 4

Step-by-step explanation:

(x, y) = (3, -1)

y = x - 4

y = 3 - 4

y = -1

#CMIIW

Jessica made 6 19/20 cups of punch. Her punch had two different types of juices in it. If the lunch had 4 1/5 cups of one type of juice, how many cups of the other type of juice did it have?

Answers

Answer:

2 3/4 cups

Step-by-step explanation:

Jessica made 6 19/20 cups of punch. Her punch had two different types of juices in it. If the lunch had 4 1/5 cups of one type of juice, how many cups of the other type of juice did it have?

We solve this question using the Subtraction operation

Total cups = cups of first type of juice + cup of other type of juice

6 19/20 = 4 1/5 cups + x

x = 6 19/20 - 4 1/5 cups

Lowest Common Denominator = 20

x = 6 - 4 + (19/20 - 1/5)

x = 2 + (19 - 4/20)

x = 2 15/20 cups

x = 2 3/4 cups

Other type of juice had 2 3/4 cups of juice

Help me with this please

Answers

Answer:

1. 5

2. 8

Step-by-step explanation:

number one is 5 and number 2 is 8

Drop your favorite American Horror Story character for 5 easy points​

Answers

Answer:

the clown plz mark brainliest

Answer:

TATE AND BROOKE THOMPSON or any of emma roberts characters

A rope is stretched from the top of a
7-foot tent pole to a point on the ground
12 ft from the base of the pole. How long
is the rope ?

Answers

Answer:

Step-by-step explanation:

we know two sides of a triangle, one side is 7 feet, the other is 12 feet , so use Pythagoras theorem

[tex]C^{2}[/tex] = [tex]A^{2}[/tex] + [tex]B^{2}[/tex]

[tex]C^{2}[/tex] = [tex]7^{2}[/tex] + [tex]12^{2}[/tex]

[tex]C^{2}[/tex] = 49 + 144

[tex]C^{2}[/tex] = 193

C = [tex]\sqrt{193}[/tex]

C = 13.89 feet

Answer:

The square of the hypotenuse equals the square of the sum of the other two sides.

13.89ft

Step-by-step explanation:

Definition Of Pythagoras Theorem :

The Pythagorean theorem states that the total of the squares on a right triangle's legs equals the square on the hypotenuse (the side opposite the right angle)—or, in popular algebraic form, a2 + b2 = c2.

Given:

Height of the Tent Pole = 7ft.

Base of the Pole of the Tent = 12ft.

Now we will use Pythagoras theorem to find how long the rope is.

Use of Pythagoras theorem

[tex]\begin{aligned}&C^{2}=A^{2}+B^{2} \\&C^{2}=7^{2}+12^{2} \\&C^{2}=49+144 \\&C^{2}=193 \\&C=\sqrt{193} \\&C=13.89 \text { feet }\end{aligned}[/tex]

Hence, the length of the rope is 13.89ft.

To know more about Pythagoras theorem here

https://brainly.com/question/343682  #SPJ2

I need to know they answers below please hurry

Answers

Answer:

A)  2

B)  0

C)  1

Step-by-step explanation:

Why can't 6cm 5cm 8cm make a triangle

Answers

Because all of the sides should be the same length.

Answer:

They can, the lines just need to be sloped

39. If one student can complete the decorations for the prom in 5 days
working alone, another student could do it in 3 days, and a third could
do it in 4 days, how long would it take them working together?

Answers

Answer:

1.3 days

Step-by-step explanation:

1/5+1/4+1/3

12/60+20/60+15/60= 47/60

60/47

=1.3

please I've been looking for an answer to this question​

Answers

Answer:

x = 9cm

using sine rule

a/sine(A) = b/sine(B)

a= x; A= 64° ( alternating angles)

b= 10 cm ; B = 90°

x/sine(64) = 10/sine(90)

x= {10 × sin(64)}/ sin 90

x = 9cm

Answer:

650

Step-by-step explanation:

A man is five times as old as his son. Four years ago the man was thirteen times as old as his son.
Find their present ages.

Answers

Answer:

Age of son = 6 years

Age of man = 5×6 = 30 years

Step-by-step explanation:

GIVEN :-

A man is 5 times as old as his son. (In Present)4 years ago , the man was 13 times as old as his son

TO FIND :-

The present ages of the man & his son.

SOLUTION :-

Let the present age of son be 'x'.

⇒ Present age of man = 5x

4 years ago ,

Age of son = (Present age of son) - 4 = x - 4

Age of man = (Present age of man) - 4 = 5x - 4

The man was thirteen times as old as his son. So,

[tex]=> 5x - 4 = 13(x - 4)[/tex]

Now , solve the equation.

Open the brackets in R.H.S.

[tex]=> 5x - 4 = 13x - 52[/tex]

Take 5x to R.H.S. and -52 to L.H.S. Also , take care of their signs because they are getting displaced from L.H.S. to R.H.S. or vice-versa.

[tex]=> 13x - 5x = 52 - 4[/tex]

[tex]=> 8x = 48[/tex]

Divide both the sides by 8

[tex]=> \frac{8x}{8} = \frac{48}{8}[/tex]

[tex]=> x = 6[/tex]

CONCLUSION :-

Age of son = 6 years

Age of man = 5×6 = 30 years

Can 1-9 be solved please ANSWER FAST!!!

Answers

Answer:

1) solution

2x+3*5x=34

2x+15x=34

17x=34

x=34/17

x=2

2) solution

2*4y+3y=44

8y+3y =44

11y=44

y=44/11

y=4

3) solution

4y+5=3y-2

4y-3y=-2-5

y= -7

4) solution

2x+3=4x-1

3+1=4x-2x

4=2x

x=4/2

x=2

5) solution

4(y-1)=3y+3

4y-1=3y+3

4y-3y=3+1

y=4

6) solution

2(1/2y +3)-y=6

2/2y+3-y=6

y+3-y=6

2y=6

y=6/2

y=3

7) solution

8x+2(-4x+11)=13

8x-8x+11=13

11=13

8) solution

2x-3x-9=-4

-x=-4+9

-x=5

x= -5

9) solution

3(3y+1)-5y=11

9y+3-5y=11

4y=11-3

y=8/4

y=2

please marks brainliest I had to spend lot of time typing this.

A swimming pool that is 10 feet, 20 feet long, and 4 1/2 feet deep. how much water can this swimming pool hold (to the top of the pool)?

Answers

Answer:

900 cubic feet

Step-by-step explanation:

Volume = length x width x height

= 10 x 20 x 4.5

= 900

in a bag, there are 5 red marbles, 2 blue marbles and 3 purple marbles. what is the probability of drawing a purple marble

Answers

Answer:

The probability of drawing a purple marble is 3/10

There are 6 red marbles, 5 green marbles, and 4 yellow marbles in a bag. If Joe picks 2
marbles one after the other without replacement, then what is the probability that both
are red in color? Are the two events independent or dependent?

Answers

30/210 simplified to 1/7 i think

Find the distance:
Speed = 99 km/h, Time = 40 mins

Answers

Step-by-step explanation:

Speed= distance/time

Speed=99 km/h /40 mins

Speed= 2,475 km/h

Answer:60km

Step-y-step explanation:

distance=Speed*Time

distance=90*(40/60)=60km

What is the fractional form of 0.02?

А. 2/99
B. 1/11
C. 2/100
D.1/12

Answers

The answer is c because the 2 is in the 100ths place

1121314 5 -
The top, front, and side views of a rectangular prism are shown.
top view
front view
(1) side view
How many unit cubes are used to build the solid?
unit cubes are used to build the solid.​

Answers

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the views are not shown.

So, I will answer this question with the attached views of a rectangular prism.

Required

The number of cubes used

For the attached views of the rectangular prism, we will make use of the following representations

Top view [tex]\to[/tex] Width

Front view [tex]\to[/tex] Height

Side view [tex]\to[/tex] Length

So, we have:

[tex]Width = 2 units[/tex]

[tex]Height = 6 units[/tex]

[tex]Length = 1\ unit[/tex]

The number of cubes is calculated by solving for the volume of the prism.

For a rectangular prism, the volume is:

[tex]Volume = Length * Width * Height[/tex]

[tex]Volume = 2 * 6 * 1[/tex]

[tex]Volume = 12[/tex]

This implies that 12 cubes were used to build the solid.

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