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2 years ago

Use an appropriate half-angle formula to find the exact value of the expression. cos(22. 5°)

Mathematics

1 answer:

Sladkaya [172]2 years ago

4 0

The value of given trigonometric value cos(22. 5°) is 0.387.

According to the statement

we have given that the trigonometric value and we have to find the exact value of that given value with the help of the half angle formula.

So, For this purpose, we know that the

The half angle formulas are used to find the exact values of the trigonometric ratios of the angles like 22.5°.

So,

The given value is :

cos(22. 5°)

Then the value of cos half angle formula is

$cos (theta/2) = +- sqrt((1-cos theta) / 2)$

then

The value of θ/2 is 22.5 degree.

And θ is 22.5*2

θ = 45 degree

and cos 45 degree is 1/squareroot 2

And by this the value of given value become is

$cos 22.5 = +\sqrt{((\sqrt{2} -1)/(2 \sqrt{2} )) } = + 0.3827$

So, The value of given trigonometric value cos(22. 5°) is 0.387.

Learn more about half angle formulas here

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Please help and thank you.

Marina CMI [18]

Answer:

400 ft elevation at 1 km and 3 km from the start
300 ft/km average rate of change over the first 4 km

length = 3.5 cm
width = 3.5 cm
height = 7.0 cm

6 mo: $1018.14
5 yrs: $1196.89
avg incr: $3.28 per month

Step-by-step explanation:

A graphing calculator is handy for solving problems involving cubic polynomials. You're interested in where the elevation is 400 ft. Since the value of f(x) is in hundreds of feet, you want to find x such that f(x) = 4.

Values of x where that is the case are x=1 and x=3, representing distances of 1 km and 3 km from the start of the road.

The average rate of change of elevation is the difference in elevation divided by the difference in distance from the start:

average rate of change = (f(4) -f(0) hundred ft)/((4 - 0) km)

= (19 -7)/4 hundred feet/km

= 12/4 hundred feet/km = 300 ft/km

___

You want to find x when ...

A(x) = 122.5 cm²

10x² = 122.5 cm² . . . . substitute the given expression for A(x)

x² = 12.25 cm² . . . . . . divide by 10

x = √(12.25 cm²) = 3.5 cm . . . . take the square root

The diagram tells you ...

length = width = x = 3.5 cm

height = 2x = 7.0 cm

___

Evaluate the given expression for the different values of m:

$1000·1.003^6 ≈ $1018.14 . . . . 6-month value

$1000·1.003^60 ≈ $1196.89 . . . . 5-year value

The increase is $1196.89 -1000.00 = $196.89. That increase took place over 60 months, so the average increase per month is ...

$196.89/(60 mo) ≈ $3.28 per mo . . . . average per month over 5 years

8 0

4 years ago

The ratio of the ages of Mandy and Sandy is 2:5. After 8 years, their ages will be in the ratio 1:2. What is the difference betw

Alchen [17]

Let $x$ represent Mandy's age and $y$ represent Sandy's.

From the first statement we have:
$5x=2y$

From the second statement we have:
$2*(x + 8) = 1*(y + 8)$

So we need to solve this system of equations:
$\left \{ {{5x=2y} \atop {2(x+8)=y+8}} \right.$

Express $y$ from first equation equation:
$2y=5x$
$y=\frac{5}{2}x$

Replace found value in second equation and solve the resulting equation:
$2(x+8)=\frac{5}{2}x+8$
$2x+16=\frac{5}{2}x+8$
$2x-\frac{5}{2}x=8-16$
$-\frac{1}{2}x=-8$
$\frac{1}{2}x=8$
$x=8*2=16$

Replace found value in first equation and solve the resulting equation:
$5*16=2y$
$2y=80$
$y=40$

So, Mandy is 16 years old and Sandy is 40 years old. The difference between their ages is 40 - 16 = 24 years.

6 0

3 years ago

Which statement is true about the expression 12-7+3

MArishka [77]

<u><em>Answer: a. associate property.</em></u>

Explanation: Associate property is a grouping in addition and multiply can be switch. But this question it's about the order of operations. It stands for p-parenthesis, e-exponents, m-multiply, d-divide, a-add, and s-subtract. It can also go left to right. (PEMDAS)

Like this: → $12-(7+3)$