Verify the Pythagorean Identity 1 + cos^2(theta) = csc^2(theta)

Answers

Answer 1

Answer: 1 + cot² t = csc² t
$1+cot ^(2) t = (1)/(sin ^(2) t) \n 1+ (cos^(2)t )/(sin^(2)t ) = (1)/(sin ^(2) t)$ / * sin² t
sin² t + cos² t = 1
1 = 1
We have confirmed the identity.

Answer 2

Answer:

The verification for the Pythagorean identity 1 + cot²∅ = cosec²∅ will lead to sin²∅ + cos²∅ = 1

How to verify Pythagorean identity?

1 + cot²∅ = cosec²∅

Therefore,

cosec²∅ = 1 / sin²∅

cot²∅ = 1 / tan²∅ = cos²∅ / sin²∅

Hence,

1 + cos²∅ / sin²∅ = 1 / sin²∅

Therefore, multiply both sides by sin²∅

1(sin²∅) + (sin²∅) cos²∅ / sin²∅ = (sin²∅) 1 / sin²∅

sin²∅ + cos²∅ = 1

learn more on Pythagorean identity here: brainly.com/question/11674053

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Please help Question on picture

Answers

Answer:

98°

Step-by-step explanation:

41° + 41° = 82°.

All triangles equal 180°.

180° - 82° = 98°

The inverse of a function is a set of ordered-pair numbers in which the range set is interchanged with the domain set. a. True
b. False

Answers

true, because it is reflected across the y=x line

Answer:

True

Step-by-step explanation:

The area of a rectangle is 507 centimeters squared. The length is 3 times the width. What is the length of the rectangle? 1) 3 cm 2) 13 cm 3) 26 cm 4) 39 cm

Answers

Answer:

option 4

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

let width be w then length = 3w ( 3 times the width )

given A = 507

substitute these values into the formula for A

507 = 3w × w , that is

507 = 3w² ( divide both sides by 3 )

169 = w² ( take square root of both sides )

$√(169)$ = $√(w^2)$ , that is

13 = w

Then

length = 3w = 3 × 13 = 39 cm

A pile of sand has a weight of 90kg.The same is put into a small bag, a medium bag and a large bag in the ratio of 2:3:7.Work out the weight of sand in each bag

Answers

Remark

This requires some sort of constant that each of the ratio members is multiplied by.

Call the constant x

Equation

2x + 3x + 7x = 90 Add the left hand side

Solution

12x = 90 Divide by 13

x = 90 /12

x = 7,5

Answer

2x = 2 * 7.5

2x = 15

3x = 22.5

7x = 52.5

Sum = 90 as it should be

A design engineer is mapping out a new neighborhood with parallel streets. If one street passes through (6, 4) and (5, 2), what is the equation for a parallel street that passes through (−2, 6)?A. y = 1 half x + 5
B. y - 1 half x + 1
C. y = 2x + 10
D. y = 2x − 14

Answers

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the first street.

$(\stackrel{x_1}{6}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{2}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{6}}} \implies \cfrac{ -2 }{ -1 } \implies 2$

so we are really looking for the equation of a line whose slope is 2 and it passes through (-2 , 6)

$(\stackrel{x_1}{-2}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \n\n\n \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\n \cline{1-1} \n y-y_1=m(x-x_1) \n\n \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{2}(x-\stackrel{x_1}{(-2)}) \implies y -6 = 2 ( x +2) \n\n\n y-6=2x+4\implies {\Large \begin{array}{llll} y=2x+10 \end{array}}$

A root of x2 – 5x – 1 = 0 is

Answers

Hello,

Roots are $(5+√(29))/(2)\ and\ (5-√(29))/(2)$

Δ=(-5)²-4*(-1)*(1)=29

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