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kykrilka [37]
4 years ago
7

Look at the triangle show on the right. The Pythagorean Theorem states that the sum of the squares of the legs of a right triang

le is equal to the square of the hypotenuse. Margaret uses this theorem to simplify and rewrite the expression (b/r)^2 + (a/r)^2 using the triangle shown. Which trigonometric identity can she prove with her expression? *
Mathematics
1 answer:
Vladimir [108]4 years ago
3 0

Answer:

cos^2\theta + sin^2\theta = 1

Step-by-step explanation:

Given

(\frac{b}{r})^2  + (\frac{a}{r})^2

Required

Use the expression to prove a trigonometry identity

The given expression is not complete until it is written as:

(\frac{b}{r})^2  + (\frac{a}{r})^2  = (\frac{r}{r})^2

Going by the Pythagoras theorem, we can assume the following.

  • a = Opposite
  • b = Adjacent
  • r = Hypothenuse

So, we have:

Sin\theta = \frac{a}{r}

Cos\theta = \frac{b}{r}

Having said that:

The expression can be further simplified as:

(\frac{b}{r})^2  + (\frac{a}{r})^2  = 1

Substitute values for sin and cos

(\frac{b}{r})^2  + (\frac{a}{r})^2  = 1 becomes

cos^2\theta + sin^2\theta = 1

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Answer:

3/4 = 0.75

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Step-by-step explanation:

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3 years ago
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Jake earns $7.50 per hour working at a local car wash. The function, ƒ(x) = 7.50x, relates the amount Jake earns to the number o
torisob [31]

For this case we have the following function:

f(x) = 7.50x

An equivalent way to write this function is:

y = 7.50x

From here, we clear the value of x.

We have then:

x = \frac{y}{7.50}

Returning the variables we have that the inverse of the function is:

f (x) ^ - 1 =\frac{x}{7.50}

Answer:

the inverse of this relation is:

f (x) ^ - 1 =\frac{x}{7.50}

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4 years ago
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What is the inverse of the function g ( x ) = − 3 ( x + 6 ) g(x)=−3(x+6)g, left parenthesis, x, right parenthesis, equals, minus
aleksley [76]

Answer:

Then inverse of the given equation is given by ,f^-1(x)=  (-x/3 - 6)

Step-by-step explanation:

Given:

Function as g(x)=-3(x+6).

To Find :

The inverse function of the g(x).

Solution:

We know that step involving to convert into inverse function as follows :

Further ,

  1. Replace g(x) with function as  "y",

             hence it becomes ,

            y=-3(x+6)

     2.Then solve for the x value ,

        it becomes as ,

      \frac{-y}{3}=x+6,

    \frac{-y}{3}-6=x

     3. Replace x with y and y with x we get ,

   \frac{-x}{3}-6=y.

it is written as ,

y=f^-1(x)=  -x/3-6

Then inverse of the given equation is given by ,f^-1(x)=  -x/3-6.

   

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4 years ago
Please help!
miv72 [106K]

Answer:

Option A. 2\ m^{2}

Step-by-step explanation:

we know that

The resulting two-dimensional cross-section is a rectangle

The area of rectangle is equal to

A=bh=1*2=2\ m^{2}

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4 years ago
What is the answer to 3x plus 5
oksian1 [2.3K]
The answer is really simple just do 3 plus 5 which is 8 so the answer is 8x
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3 years ago
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