prove that -
[tex] \sin {}^{2} (\theta) + \cos {}^{2} (\theta) = 1[/tex]

ty !​

Answers

Answer 1

Answer:

Step-by-step explanation

There are many ways to prove this identity. But, I will use the simplest one. If you have a right triangle, the length of the horizontal side is x, the length of the vertical side is y, and the hypotenuse is r. So, the relation between x and r can be written in cosine form:

[tex]\cos\theta=\frac{x}{r}[/tex]

The relation between y and r can be written in sine form:

[tex]\sin\theta=\frac{y}{r}[/tex]

Pythagoras told you that for the right triangle [tex]x^{2}+y^{2}=r^{2}[/tex] should be satisfied. Substitute x and y from the cosine and sine form:

[tex](r\cos\theta)^{2}+(r\sin\theta)^{2}=r^{2}[/tex]

[tex]r^{2}\cos^{2}\theta+r^{2}\sin^{2}\theta =r^{2}[/tex]

the square of r will cancel out, and you can get your identity:

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


Related Questions

i have 120g butter and 150g sugar.

1) what’s the ratio of butter to sugar?

2) what’s the ratio in the form 1:n ?

Answers

Answer:

1) 4 : 5

2) 1 : 5/4

.................................

rearrange so u Rearrange the equation so www is the independent variable.
−2u+6w=9

Answers

6w = 9 + 2u
w = 9 + 2u / 6

Answer:

w=9+2u/6

Step-by-step explanation:

-2u+6w=9

+2u on both sides

6w=9+2u

/6 on both sides

w=9+2u/6

Convert the fraction 23/
12
into decimal​

Answers

Answer:

1.916 just devide: 23÷12=1.916

Answer:

[tex]1.917[/tex]

Step-by-step explanation:

[tex] \frac{23}{12} \frac{ \times8.33333333 }{ \times 8.33333333} \\ = \frac{191.666667}{100} \\ = 1.917[/tex]

x2-30x+81

Answer (x-27)(x-3)

Answers

The answer is (x-27)(x-3) in factored form. The answer using the quadratic formula is x= 27,3

Please help me with this coordinate geometry homework !!!!

Answers

Answer:

Step-by-step explanation:

a. Gradient of A = 7/-7 = -1.

b. For line B, m = 3/1.5 = 2 and c = y-intercept = 3.

c. The line parallel to B will have the same gradient m = 2.

It also passes through (1, -1) so we use the point-slope form of the straight line

y - y1 = m(x - x1)

Here m = 2 and (x1, y1) = (1, -1) so

y - (-1) = 2(x - 1)

y = 2x - 2 - 1

y = 2x -3.

help i give brianlyist and 5 star rating whith heart

Answers

Answer:

26

Step-by-step explanation:

perimeter is sum of all sides

11+7+4+4=perimeter

26

Solve the following equation.
25z^2+93 = 100z

Answers

Step-by-step explanation:

25z square+93=100z

=25z square+93=10z square

=25z square-10z square=-93

=15z square= -93

Please help! Geometry Dilations, Similar triangles & proportionality

Answers

9514 1404 393

Answer:

  ? = 8

Step-by-step explanation:

The parallel lines divide the segments proportionally:

  ?/4 = 10/5

  ? = 4(10/5) = 8 . . . . multiply by 4

The missing length is 8.

please help me ..............

Answers

Answer: A, C, E

Step-by-step explanation:

An undefined slope means the line is vertical (and thus the x-coordinates are constant).

Which lists all the factors of 20? *
1 point
2, 4, 5
20, 40, 60
1, 2, 4, 5, 10, 20
5, 10, 15, 20

Answers

Answer:

C

Step-by-step explanation:

A is incorrect because it doesn't list all of the factors of 20.

B is incorrect because it is listing the multiples of 20.

D is incorrect because is doesn't list all of the factors of 20.

Figure ABCD is a parallelogram.What is the value of n?3 5 17 25

Answers

Answer:

17

Step-by-step explanation:

∠B = ∠D

2n + 32 = 4n - 2

32 + 2 = 4n - 2n

2n = 34

n = 17

g (x) = x2 + 12x-
35

Answers

Answer:

not factorable

Step-by-step explanation:

g(x) = x²+12x-35

Not factorable

Sid Upp is four years younger than his brother Tip. Let x stand for Tip's age . Write an equation stating that Sid's age is 32.

Answers

Answer:

x+4=36

Step-by-step explanation:

you would subtract 4 on each side

x+4=36

  -4   -4

x=32

MATHEMATICAL CONNECTIONS The volume of a cylinder is given by V=pi r^2h, where r is the radius of the base of the cylinder and h is the height of the cylinder. Find the dimensions of the cylinder. the radius is h-3 and the volume is 25h*pi

Answers

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=h-3\\ V=25h\pi \end{cases}\implies 25h\pi =\pi (h-3)^2 h \\\\\\ \cfrac{25h\pi }{\pi h }=(h-3)(h-3)h\implies 25=\stackrel{F~O~I~L}{h^2-6h+9}\implies 0=h^2-6h-16 \\\\\\ 0=(h-8)(h+2)\implies \blacktriangleright h= \begin{cases} 8~~\checkmark\\ -2 \end{cases} \blacktriangleleft ~\hfill \blacktriangleright \underset{radius}{\stackrel{8~~ - ~~3}{5}} \blacktriangleleft[/tex]

notice, we didn't use h = -2, because the height cannot be a negative value.

in which quadrant is the point (4,-2 located

Answers

Answer:

quadrant 4

Step-by-step explanation:

Hope this helped :)

also can you pls rate thanks

Answer:

The point is located in the fourth quadrant.

Step-by-step explanation:

I'm pretty sure it that. Hope its right!

The Red Shell's flight path is modeled by the equation:
y = -2x2 + 60x + 350
a) Factor the equation below:
olutions to the equation?

Answers

Answer:

Geometric figure: Straight Line

Slope = 120.000/2.000 = 60.000

x-intercept = 346/-60 = 173/-30 = -5.76667

y-intercept = 346/1 = 346.00000

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

y-(-4+60*x+350)=0

STEP

1

:

Equation of a Straight Line

1.1 Solve y-60x-346 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line y-60x-346 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 346/1 so this line "cuts" the y axis at y=346.00000

y-intercept = 346/1 = 346.00000

Calculate the X-Intercept :

When y = 0 the value of x is 173/-30 Our line therefore "cuts" the x axis at x=-5.76667

x-intercept = 346/-60 = 173/-30 = -5.76667

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 346.000 and for x=2.000, the value of y is 466.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 466.000 - 346.000 = 120.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 120.000/2.000 = 60.000

Geometric figure: Straight Line

Slope = 120.000/2.000 = 60.000

x-intercept = 346/-60 = 173/-30 = -5.76667

y-intercept = 346/1 = 346.00000


PLEASE HELP!!! ILL GIVE BRANLIEST *EXTRA POINTS* dont skip :((

Answers

Answer:

75%

Step-by-step explanation:

math go brr

The value of each expression if x=12
3x

Answers

Answer:

3*12=36

hope thats the answer

PLEASEEEE HELP!!!!!!!!!!!

Answers

Answer:

yes

Step-by-step explanation:

The question has been posted below:

Answers

Answer:

Step-by-step explanation:

b:)

The area in square feet of a rectangular field is
x2 – 120x + 3500. The width, in feet, is x-50. What is the
length, in feet?

Answers

Answer:

Length in feet:  x-70

Step-by-step explanation:

Use factorization to find the length

Area = X^2-120x+3500

Area= length x width.

Area= L x (x-50)= (x-___) (x-50)

To find L we know that in factoring the quadratic equation 50 x __ must be equal to 3500.

(x-70)(x-50) = x^2-120x+3500.

is 3 8/33 equivalent to the decimal 3.24 (repeating)

Answers

Answer:

Yes it is

Step-by-step explanation:

8 ÷ 33 = .242424( infinite )

Add the beginning 3 to it and you get 3.24 (repeating)

Hope this helps.

yes it is equivalent

Is this scientific notation
42,060=4.206 x 10 to the 4th

Answers

Answer:

yes it is scientific notation

These points are linear.
Find the slope.

x -2 -1 0 1 2
y -7 0 7 14 21

Answers

Answer:

7

Step-by-step explanation:

use the equation y2 - y1/ x2 - x1 to find the slope

-7 - 0/-2 - (-1)

-7/-1
7

y = 7x + b

if you want to check we have to find the y-intercept

(i can also show how to find it if you want :D)

a farmer sells 8.6 kilograms of pears and apples at the market.1/4 of this weight are pears the rest are apples. How many kilograms of apples did she sell at the farmers market?

Answers

Step-by-step explanation:

8.6÷1/4 = 34.4

#Ihopethishelps

PLEASE HELP! WILL GIVE BRAINLIEST

Answers

Answer:

b

Step-by-step explanation:

if you put

[tex] \times = 0 \\[/tex]

and check the values

function b gives highest value

please help, i did 90 - 10 and I got 80. I’m stuck at 80

Answers

Answer:

approx 216

Step-by-step explanation:

well we go to the 10mm mark and we add the columns taht appear before that. Those are two columns : the brown/orangey one and the green one.

if the scale goes up in twenty and each jump has four squares then we can say that one square is equal to 5 up

so we now can read the first two columns

the first one reads 135

the second one reads approximately 81

we add those up and that becomes 216

so the answer is approximately 216

a cylinder has an approimate 1357.1 cubic yards. the raduis of the cylinder is 6 yards. what is the height of the cylinder

Answers

Answer:

Step-by-step explanation:

Find the radius and height. ...

Convert inches to yards, convert feet to yards, or convert meters to yards.

Multiply the radius of the cylinder times the radius, e.g. r2

Multiply times π to get the area of the circle.

Multiply times the height of the cylinder to get the volume.

After Lydia spends 20% of her savings on car repairs, she has $1500 left. How much was in her saving originally?

Answers

Answer:

$7,500

Step-by-step explanation:

1500/2 750, 750x10=7,500

A triangle has an area of 35 cm squared. The BASE of the triangle is (x-5) cm and the HEIGHT of the triangle is (x-14) cm. Find the measure of the HEIGHT and BASE.

Answers

Try to use this method and see if you get the answer

Step-by-step explanation:

area = b * h / 2 , where b is a base, h - height.

so h = 2 * area / b.

Other Questions
1. A surfboarder rides a wave for 23.7 m at a constant rate of 4.1 m/s. How long did his triptake? Jerry is terrified of snakes, even though he lives in midtown Manhattan and only sees snakes at pet shops and zoos. He is probably suffering from When operating a crane, which of the following is an important safety precaution? Select all that apply.Select the 3 answer options that apply.Ensure that all worksite personnel are qualified crane operatorsCheck for overhead power linesEnsure your area of travel is clearNever lift people ANSWER PLS!!!!!!!!!!!Is there a different way to balance a synthesis, decomposition, single displacement and double displacement reactions or is it all the same chala goes to school a.everyday b.once aweek c.once a month 16. What force is needed to accelerate a 500 kg object at a rate of 10 m/s2?*(3 Points) In the call of the wild before buck attempted to break out of the frozen 1000 pounds lead load John Thorton whispered to him as you love me why did this seem like a conjuration to the crowd What was one weakness of the Articles of Confederation in establishing the first government of the United States? Question 2 options: Counting votes took too long because each state had seven representatives. Larger states had more power than smaller states. Taxes were set at the British rate in order to cover the costs of the war. Any measure required nine states for approval and amendments required all thirteen. What plan allows a company to take money out of a paycheck and put it into a savings account for an employee?1. insurance plan2. 401K3. vacation plan4. paid time off You can work a total of no more than 10 hours each week at your iwo jobs. House cleaning pays $5 per hour andyour sales job pays $8 per hour. You need to earn at least $56 each week to pay your bills. Write a system ofinequalities that show the various numbers of hours you can work at each job. Which of the following are factor pairs for 72? You will select two. 2 x 363 x 186 x 128 x 8 HELP ASAP!!!!!! 3 SENTENCES PLEASEwhat is the structure of proteins? What is 2 to the x power Which one of these Supreme Court cases had the BIGGEST impact on the beginning of the "Jim Crow" era?A) Plessy v. Ferguson B) Worcester v. Georgia C) United States v. Nixon D) Brown v. Board of Education Attributing physical illness signs and symptoms to a psychiatric condition is referred to as. What does number 8 wire mean to New Zealanders? Firefox won't play my downloaded videos, how do I fix that how could entrepreneurship help school leavers not to become an unemployment statistic Which of the following types of forces is NOT an active force.A. Tensional Force B. Applied ForceC. Gravitational ForceD. Friction Force How does the negative feedback system of the parathyroidglands differ from that of the thyroid gland?