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Pepsi [2]
3 years ago
13

What geometric principal allows us to define trigonometric functions as ratios of sides of triangles and be confident that they

are indeed functions? That is, how do we know that the value of each angle put into a trigonometric function results in exactly one output value?
Mathematics
2 answers:
slavikrds [6]3 years ago
8 0
Two geometrical objects are called similar if they both have the same shape, or one has the ... Due to this theorem, several authors simplify the definition of similar triangles<span> to only require that the corresponding three angles are congruent. I hope that helps you.</span>
mash [69]3 years ago
3 0

Solution:

The  geometric principal which allows us to define trigonometric functions as ratios of sides of triangles and they are indeed functions

1. Similarity of Two Right Triangles

2. Concept of unit circle

→→As a complete circle means angle of π radians or an angle of 360°.So if you take any of trigonometric function and any right angled triangle , you will find that for angle between 0°≤Ф≤90°, values of trigonometric functions are different.Because for each angle, ratio of side lengths of right angled triangle changes, that's why for each unique angle we get a unique output value for different trigonometric functions.

You can call it  one-one onto mapping (function) also.


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An architect designs a rectangular flower garden such that the width is exactly​ two-thirds of the length. if 370 feet of antiqu
Korolek [52]

Answer:

111 Feet

Step-by-step explanation:

The feet of antique picket fencing are to be used to enclose the​ garden is equivalent to the perimeter of the flower garden.

The perimeter P of a rectangle  whose length is L and width is W is given as

P = 2( L + W)

Given that the width is exactly​ two-thirds of the length

then, W = 2/3 L and P = 370 feet

L = 3/2 W = 1.5W

370 = 2 ( 1.5W + W)

370 = 5W

W = 370/5

= 74 Feet

L = 1.5W

= 1.5 * 74

= 111 Feet

6 0
4 years ago
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Each shape is 1 whole. Which fraction greater than 1 names the parts that are shaded
Nutka1998 [239]
You have no pictures of the shapes?
6 0
3 years ago
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Simplify. (−6)^2 please help
disa [49]

Note that (-6)^2 = (-6)(-6)

Multiply across. Remember that when multiplying two negative numbers, the product would be a positive answer

(-6) x (-6) = 36

36 is your answer

~<em>Rise Above the Ordinary, Senpai</em>


8 0
3 years ago
Read 2 more answers
Evaluate the geometric series
JulijaS [17]

Answer:

Option B is correct.

sum of given geometric series is, 255

Step-by-step explanation:

Evaluate the geometric series: \sum_{i=1}^{8} 2^{i-1}

we can write this as:

1+2+4+.......+128

Formula for the sum of the geometric series:

S_n = \frac{a(r^n-1)}{r-1} for r > 1

where

a is the first term

n is the number of terms

r is the common ratio

In the given series:

common ratio (r) = 2>1, n = 8 and first term(a) = 1

Since,

\frac{2}{1} = 2

\frac{4}{2} = 2 and so on...

then substitute the given values in [1] we have;

S_n = \frac{1((2)^8-1)}{2-1}

or

S_n = 256-1 = 255

Therefore, the sum of given geometric series is, 255



6 0
3 years ago
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Which of the following expressions are equivalent to
dmitriy555 [2]

Answer:

A

Step-by-step explanation:

7 0
3 years ago
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