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Answer:
The Pythagorean identity [tex]\sin^2\theta+\cos^2\theta=1[/tex] comes from Pythagorean theorem and the unit circle. In the unit circle, for any point on the circle, there y-coordinate represents the sine of the angle and the x-coordinate represents the cosine of the angle. For any angle [tex]\theta[/tex], we can create a right triangle using the x-coordinate and y-coordinate as legs of the triangle. The hypotenuse of this triangle would be the radius of the unit circle, which is given as 1.
The Pythagorean theorem states that in all right triangles, the following must be true:
[tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle and [tex]a[/tex] and [tex]b[/tex] are two legs of the triangle.
Therefore, we have the following equation:
[tex](\sin\theta)^2+(\cos\theta)^2=1^2,\\\boxed{\sin^2\theta+\cos^2\theta=1}[/tex]
The Pythagorean identity comes from Pythagorean theorem and the unit circle. In the unit circle, for any point on the circle, there y-coordinate represents the sine of the angle and the x-coordinate represents the cosine of the angle. For any angle , we can create a right triangle using the x-coordinate and y-coordinate as legs of the triangle. The hypotenuse of this triangle would be the radius of the unit circle, which is given as 1.
The Pythagorean theorem states that in all right triangles, the following must be true:
, where is the hypotenuse of the triangle and and are two legs of the triangle.
Therefore, we have the following equation:
Related Questions
CD is the Diameter. The measure of Arc CD is 11x Find the length of the radius in the circle.
Answers
Answer:
11
Step-by-step explanation:
Using S = rA, where S is arc length, r is radius and A is angle(in radians).
Comparing: S = 11π, A = 180° = π
=> 11π = rπ
=> 11 = r
Required radius is 11 unit
Method 2:
This is a semi circle, circumference of semi circle is πr, so
πr = 11π
r = 11
PLEASE PLEASE HELP ME ASAP
Answers
Answer:
378
Step-by-step explanation:
540 of 70%. So you will write this as 70 / 100 x 540 = 378. I hope this helped you.! <3
PLAEASE Help If you answer this right I will mark you brainlist
Answers
Answer:
Hello! answer: 65
Step-by-step explanation:
This is a supplementary angle meaning it will add up to 180 degrees therefore... 180 - 115 = 65 therefore x = 65 hope that helps!
Answer:
x=65°
Step-by-step explanation:
180°= x + 115°
x = 180 - 115
x = 65°
Solve for X. rx-s = t
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Answer: x=t/r+s/r
How to: Isolate the variable by dividing each side by factors that don't contain the variable.
Have a great day and stay safe !
Answer:
[tex]solve \: \: for \: \: x \\ rx - s = t \\ rx = t + s \\ x = \frac{t + s}{r} [/tex]
what is 2/3 - 1/3 I appreciate all answers!! (btw i dont wanna do all the math right now so i know how to do it i am just not in the mood of doing it rn.)
Answers
Answer:
1/3
Step-by-step explanation:
2/3-1/3=1/3
#Carry on Learning
[tex]0.333[/tex] ✅
Step-by-step explanation:
[tex] \frac{2}{3} - \frac{1}{3} \\ = \frac{2 - 1}{3} \\ = \frac{1}{3} \\ = 0.333[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning}}{\orange{.}}}}}[/tex]
The two windows shown are similar. What is the height of the larger window?
Answers
Find y.
Write your answer in simplest radical form.
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Answer:
y = 6
Step-by-step explanation:
in a 45-45-90 triangle, the hypotenuse is [tex]\sqrt{2}[/tex] multiplied by the side across from the 45° angle
Multiply as a decimal point
0.6 x 0.4 =
Answers
Answer:2.4
Step-by-step explanation:
Solve for x. (-6/5) x - 4 = -46
A: 23
B: 35
C: -23
D: -35
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Answer:
you have flvs? am if u do is it geometry?
Find h(x+2) if h(x) = 9x-16
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Rajiv brought 1325 packs of red balls 1238 packs of yellow balls and 1334 packs of green balls there were 6 balls in each pack how many balls did rajiv buy .Change the numbers to very simple numbers in UPSL method
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Answer:
Rajiv bought 23,382 balls.
Step-by-step explanation:
Given that Rajiv bought 1325 packs of red balls, 1238 packs of yellow balls and 1334 packs of green balls, and there were 6 balls in each pack, to determine how many balls did Rajiv buy the following calculation must be performed:
(1,325 + 1,238 + 1,334) x 6 = X
3.897 x 6 = X
23.382 = X
Therefore, Rajiv bought 23,382 balls.
using the 45o −45o −90o Triangle theorem.
Solve this triangle.
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Find the length of the missing leg.
Answers
Answer:
Step-by-step explanation:
using formula
a^2+b^2=c^2
x^2+4^2=8^2
x^2+16=64
x^2=64-16
x=[tex]\sqrt{48}[/tex] cm
Answer:
x = [tex]\sqrt{48}[/tex]
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
x² + 4² = 8²
x² + 16 = 64 ( subtract 16 from both sides )
x² = 48 ( take the square root of both sides )
x = [tex]\sqrt{48}[/tex]
At Simba Travel Agency, the price of a climbing trip to Mount Kilimanjaro includes an initial fee plus a constant fee per meter. FFF represents the fee (in dollars) for climbing ddd meters. F=110+0.12dF=110+0.12dF, equals, 110, plus, 0, point, 12, d What is the increase in price for every 100100100 meters climbed?
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Answer:
122fee/meter
Step-by-step explanation:
Given the expression for the initial fee plus a constant fee per meter expressed as;
F = 110 + 0.12d
Is d = 100m
Substiutte into the expression and get F
F = 110 + 0.12(100)
F = 110 + 12
F = 122
Hence the required increase in price is 122fee/meter
Answer:
110
Step-by-step explanation:
KInda need to hurry first answer gets brainlist
Answers
Answer: d
Step-by-step explanation:
Answer:
I think the answer to your question is 3x-5y^2 i am not sure.
Step-by-step explanation:
I hope this helps, have a nice day
you roll a six sided dice 60 times the number for which the experimental probability of rolling the number is the same as the theoretical probability is
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Answer:
The answer is "12 times, a die was rolled. Identify the complete possibilities to roll exactly 6".
Step-by-step explanation:
Using formula:
[tex]P(X=K)=\binom{N}{K} P^{K} a^{N-K}[/tex]
So the value is [tex]P(X=6)[/tex]
Please help me I really need this
Answers
Answer:
y-intercept = 2 so it’s the first answer option
Step-by-step explanation: How to find the slope. Slope is rise/run so choose one point on the graph, and figure out how many squares it goes up and how many over, that’s your slope. Then, to find the y-intercept, find the point where it intersects on the y-axis, in this case it looks like 2.
Equations from tables
Plzz help
Answers
Rate of change: 3
Equation: y + 3
2. Initial value: 3
Rate of change: 3
Equation: y + 3
3. Initial value: 8
Rate of change: -2
Equation: y - 2
The initial value is the y-coordinate when x is equal to 0.
The rate of change is the difference between one point to the next immediate point.
The equation shows the rate of change.
Which of the following is most likely the next step in the series?
Look at the photo
Answers
what is the surface area of a box with measurements length = 5.7 height = 8.5 and width = 1.9? I forgot what surface area is so I need help
Answers
Answer:
150.86
Step-by-step explanation:
to calculate the surface area the formula is 2(wl+hl+hw). Hope I helped!
HELP ME OUT PLEASEEEEEEEEEEEe
Answers
Step-by-step explanation:
y = 15× tan25° = 15×0.466 = 6.99 m
r (Hypotenuse) = 15/cos25° = 15/0.906
= 16.56m
the total height = 6.99+16.56 = 23.55 m
A bag contains 8 apples and 6 oranges. You randomly draw a piece of fruit from the bag, eat it, and then randomly draw another. What is the probability you draw and eat an apple then draw an orange
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Answer:
probability of choosing apple first = 8/14
probability of choosing orange second = 6/13
probability of choosing apple and orange = 8/14 x 6/13 = 24/91
Step-by-step explanation:
What is another way to write this??
Answers
Answer:
b is the answer
....................
Answer:
B.
Step-by-step explanation:
The negative (-) must be within the parentheses “(..)”. The expression is repeated four times, thus (-2/3)^4
can you please help !
Answers
The sides of a triangle are 2x+4, 5x+2, and 4x-3. What is the perimeter if x=2
Answers
Answer:
25
Step-by-step explanation:
The three sides of a triangle are 2x+4, 5x+2, and 4x-3.
The sum is the perimeter
P = 2x+4+ 5x+2+ 4x-3
Combine like terms
P = 11x +3
Let x =2
P = 11*2 +3
P = 22+3
P =25
Answer:
25
Step-by-step explanation:
Side 1: 2x+4 Side 2: 5x+2 Side 3: 4x-3
Substitute-
2(2)+4 5(2)+2 4(2)-3
Multiply-
4+4 10+2 8-3
Combine Terms-
16 + 12 + 5
=25
SOMEONE PLEASE HELP ME! I promise i will mark brainlest, but i need the right answer for this. help is much appreciated <3
Answers
CCCCCCC
the best answer
Answer: the second one well because... i dont know how to explain it
How do I find the volume?
Answers
Answer:
425 ft³
Step-by-step explanation
Find the volume of the entire figure, if the part wasn't cut out
It would be 11 x 8 x 5 = 440
Now do 5 x 1 x 3 = 15
440 - 15 = 425
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
A sphere has a volume of 972π cm3. What is its radius in centimeters
Answers
Answer:
radius = 6.15
Step-by-step explanation:
cuz ik can u mark me brainliest?
(trigonometry) solve for x
Answers
Answer:
x= about 36.9
Step-by-step explanation:
We have 2 known factors, the degree of 31 and 19 for a side.
19 and x are opposite and hypotenuse of the angle of 31.
sin 31 = 19/x
We isolate and do
19/sin 31
The triangle below is isosceles. Find the length of side x in simplest radical form with
a rational denominator.
х
6
Answers
Step-by-step explanation:
it's the square equal to the equivalent equation to equal 5 673y