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3 years ago

I need help on this please!!

Mathematics

1 answer:

Gwar [14]3 years ago

3 0

Answer:

Step-by-step explanation:

Using the trigonometric identity

csc x = $\frac{1}{sinx}$

Given

sinΘ = - 0.4, then

cscΘ = $\frac{1}{-0.4}$ = - 2.5 → C

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1. Derive the half-angle formulas from the double

lilavasa [31]

1) cos (θ / 2) = √[(1 + cos θ) / 2], sin (θ / 2) = √[(1 - cos θ) / 2], tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]

2) (x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).

3) The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°). The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).

4) The linear function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).

<h3>How to apply trigonometry on deriving formulas and transforming points</h3>

1) The following trigonometric formulae are used to derive the half-angle formulas:

sin² θ / 2 + cos² θ / 2 = 1 (1)

cos θ = cos² (θ / 2) - sin² (θ / 2) (2)

First, we derive the formula for the sine of a half angle:

cos θ = 2 · cos² (θ / 2) - 1

cos² (θ / 2) = (1 + cos θ) / 2

cos (θ / 2) = √[(1 + cos θ) / 2]

Second, we derive the formula for the cosine of a half angle:

cos θ = 1 - 2 · sin² (θ / 2)

2 · sin² (θ / 2) = 1 - cos θ

sin² (θ / 2) = (1 - cos θ) / 2

sin (θ / 2) = √[(1 - cos θ) / 2]

Third, we derive the formula for the tangent of a half angle:

tan (θ / 2) = sin (θ / 2) / cos (θ / 2)

tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]

2) The formulae for the conversion of coordinates in rectangular form to polar form are obtained by trigonometric functions:

(x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).

3) Let be the point (x, y) = (2, 3), the coordinates in polar form are:

r = √(2² + 3²)

r = √13

θ = atan(3 / 2)

θ ≈ 56.309°

The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°).

Let be the point (r, θ) = (4, 30°), the coordinates in rectangular form are:

(x, y) = (4 · cos 30°, 4 · sin 30°)

(x, y) = (2√3, 2)

The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).

4) Let be the linear function y = 5 · x - 8, we proceed to use the following substitution formulas: x = r · cos θ, y = r · sin θ

r · sin θ = 5 · r · cos θ - 8

r · sin θ - 5 · r · cos θ = - 8

r · (sin θ - 5 · cos θ) = - 8

r = - 8 / (sin θ - 5 · cos θ)

The linear function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).

To learn more on trigonometric expressions: brainly.com/question/14746686

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4 0

1 year ago

Please pick one of the options.

olchik [2.2K]

9880 different possibilities are there in Sally's new combination option second 9880 is correct.

<h3>What is permutation and combination?</h3>

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

We have:

Total unique numbers consists in a Sally locker = 3

From the digits 0 to 39

Total numbers = 40

Apply combination formula:

= C(40, 3)

= 40!/(3!37!)

= 9880

Thus, 9880 different possibilities are there in Sally's new combination option second 9880 is correct.

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6 0

1 year ago

A pilot is flying a CRJ-900 from Phoenix, Arizona, to Louisville, Kentucky. The aircraft cannot take off or land if the temperat

ioda

We need to find an inequality that represents the possible landing or take of conditions of an aircraft, the required graph and one case where the inequality will be tested.

The required inequality is $-40$ .

The graph represents the allowable temperature range in which the aircraft can takeoff or land.

The pilot could not have taken off on June 1990, the temperature in Phoenix, Arizona.

Let the temperature be denoted by $x$

The temperature cannot be at or below $-40^{\circ}\text{F}$ , so

$x>-40$

The temperature cannot be at or above $118^{\circ}\text{F}$ , so

$x$

The inequality will be $-40$ .

In the graph it can be seen that all points between -40 and 118 falls in the shaded region but it will exclude the points -40 and 118.

The graph represents the allowable temperature range in which the aircraft can takeoff or land.

The temperature in June 1990 in Phoenix, Arizona was $122^{\circ}$ which is more than $118^{\circ}\text{F}$ .

Hence, the pilot could not have taken off on this day.

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4 0

1 year ago

PLEASE HELP I'LL GIVE YOU POINT PLEASE GEOMETRY WORK

Monica [59]

Answer:

I: 82.1

Step-by-step explanation:

4 0

2 years ago

57% people ordered steak. 120 did not. how many customers were there that night?

jok3333 [9.3K]

X - number of customers

$120+57\%x=x\\
120+0.57x=x\\
0.43x=120\\
x\approx297.07$

There can't be a fraction of the number of people, so there must be some mistake in the question.

4 0

2 years ago