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Lunna [17]
3 years ago
7

Given the following trigonometric ratio, enumerate the meaning ratio ​

Mathematics
1 answer:
Likurg_2 [28]3 years ago
6 0

Answer:

The trigonometric ratios are presented below:

\sin \theta = \frac{AC}{\sqrt{AC^{2} + BC^{2}}}

\cos \theta = \frac{BC}{\sqrt{AC^{2} + BC^{2}}}

\cot \theta = \frac{BC}{AC}

\sec \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{BC}

\csc \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{AC}

Step-by-step explanation:

From Trigonometry we know the following definitions for each trigonometric ratio:

Sine

\sin \theta = \frac{y}{h} (1)

Cosine

\cos \theta = \frac{x}{h} (2)

Tangent

\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{y}{x} (3)

Cotangent

\cot \theta = \frac{\cos \theta}{\sin \theta} = \frac{x}{y} (4)

Secant

\sec \theta = \frac{1}{\cos \theta} = \frac{h}{x} (5)

Cosecant

\csc \theta = \frac{1}{\sin \theta} = \frac{h}{y} (6)

Where:

x - Adjacent leg.

y - Opposite leg.

h - Hypotenuse.

The length of the hypotenuse is determined by the Pythagorean Theorem:

h = \sqrt{x^{2}+y^{2}}

If y = AC and x = BC, then the trigonometric ratios are presented below:

\sin \theta = \frac{AC}{\sqrt{AC^{2} + BC^{2}}}

\cos \theta = \frac{BC}{\sqrt{AC^{2} + BC^{2}}}

\cot \theta = \frac{BC}{AC}

\sec \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{BC}

\csc \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{AC}

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If the Internet consisted of four computers, there would be six possible connections. If it consisted of five computers, there w
Luba_88 [7]

Answer:

<em>45 possible connections</em>

<em />

Step-by-step explanation:

The general equation for finding the possible number of connections in a network is given as

\frac{n*(n - 1)}{2}

where n is the number of computers on the network.

for 4 computers, we'll have

\frac{4*(4 - 1)}{2} = \frac{4*3}{2} = 6

for 5 computers, we'll have

\frac{5*(5 - 1)}{2} = \frac{5*4}{2} = 10.

therefore, for 10 computers, we will have

\frac{10*(10 - 1)}{2} = \frac{10*9}{2} = <em>45 possible connections</em>

3 0
3 years ago
The average cost of tuition and room and board at a small private liberal arts college is reported to be $8,500 per term, but a
Tom [10]

Answer:

H₀: µ ≤ $8,500; H₁: µ > $8,500

z= +1.645

Step-by-step explanation:

From the given problem  As average cost of tuition and room and board at a small private liberal is less than the financial administrator As hypothesis is true.

As standard deviation is $ 1,200

α = 0.05

H₀: µ ≤ $8,500

if the null hypothesis is true then value for critical z is +1.645.

6 0
2 years ago
Devon is 30 years older than his son, Milan. The sum of both their ages is 48. Using the variables d and m to represent the ages
statuscvo [17]

Answer+Step-by-step explanation:

m = man's age

s = son's age

m=s+36

(m+8)=3*(s+8)

Resolves to: s=10, m=46

So the man is 46 (=10+36).

In 8 years, son is 18 (=10+8), man is 54 (=3*18 and 46+8), thank you.

5 0
2 years ago
The circumference of a circle is 9 pi.What is the area,in square inches,of a circle?Express your answer in terms of pi.
Alla [95]

Answer:

20.25π

Step-by-step explanation:

The circumference (C) of a circle is calculated using the formula

C = 2πr ← r is the radius

given C = 9π, then

2πr = 9π ( divide both sides by 2π )

r = \frac{9\pi }{2\pi } ( cancel the π on numerator/denominator )

  = 4.5

The area (A) of a circle is calculated using the formula

A = πr² = π × 4.5² = 20.25π

5 0
3 years ago
The probability that a randomly selected 2 2​-year-old male garter snake garter snake will live to be 3 3 years old is 0.98861 0
Mnenie [13.5K]

Answer:

a. Probability = 0.97735

b. Probability = 0.92294

c. P(At\ Least\ One) = 1

No, it is not unusual if at least 1 lives up to 3.

Step-by-step explanation:

Given

Represent the probability that a 2 year old snake will live to 3 with P(Live);

P(Live) = 0.98861

Solving (a): Probability that two selected will live to 3 years.

Both snakes have a chance of 0.98861 to live up to 3 years.

So, the required probability is:

Probability = P(Live)\ and\ P(Live)

Probability = 0.98861 * 0.98861

Probability = 0.9773497321

Probability = 0.97735 <em>--- Approximated</em>

Solving (b): Probability that seven selected will live to 3 years.

All 7 snakes have a chance of 0.98861 to live up to 3 years.

So, the required probability is:

Probability = P(Live)^n

Where n = 7

Probability = 0.98861^7

Probability = 0.92294324145

Probability = 0.92294 <em>--- Approximated</em>

Solving (c): Probability that at least one of seven selected will not live to 3 years.

In probabilities, the following relationship exist:

P(At\ Least\ One) = 1 - P(None).

So, first we need to calculate the probability that none of the 7 lived up to 3.

If the probability that one lived up to 3 years is 0.98861, then the probability than one do not live up to 3 years is 1 - 0.98861

This gives:

P(Not\ Live) = 0.01139

The probability that none of the 7 lives up to 3 is:

P(None) = P(Not\ Live)^7

P(None) = 0.01139^7

Substitute this value for P(None) in

P(At\ Least\ One) = 1 - P(None).

P(At\ Least\ One) = 1 - 0.01139^7

P(At\ Least\ One) = 0.99999999999997513055642436060443621

P(At\ Least\ One) = 1 ---- Approximated

No, it is not unusual if at least 1 lives up to 3.

This is so because the above results, which is 1 shows that it is very likely for at least one of the seven to live up to 3 years

7 0
3 years ago
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