MATHEMATICS COLLEGE

- Use the unit circle to evaluate
the six trigonometric functions
of theta= 4pi

Answers

Answer 1

Answer:

The six trigonometric functions, $\sin (\pi)/(4) =(1)/(√(2))$ , $\cos (\pi)/(4) =(1)/(√(2))$ , $\tan (\pi)/(4) =1$ , $\cot (\pi)/(4) =1$ , $\sec (\pi)/(4) =√(2)$ and $\csc (\pi)/(4) =√(2)$ .

Step-by-step explanation:

We have,

$(\pi)/(4)$

To write the six trigonometric functions = ?

$\sin (\pi)/(4) =(1)/(√(2))$

$\cos (\pi)/(4) =(1)/(√(2))$

$\tan (\pi)/(4) =1$

$\cot (\pi)/(4) =1$

$\sec (\pi)/(4) =√(2)$

$\csc (\pi)/(4) =√(2)$

∴ The six trigonometric functions, $\sin (\pi)/(4) =(1)/(√(2))$ , $\cos (\pi)/(4) =(1)/(√(2))$ , $\tan (\pi)/(4) =1$ , $\cot (\pi)/(4) =1$ , $\sec (\pi)/(4) =√(2)$ and $\csc (\pi)/(4) =√(2)$ .

Related Questions

• Water tank A has 220 gallons of water and is being drained at a constant rate of 5 gallons per minute.• Water tank B has 180 gallons of water and is being drained at a constant rate of 3 gallons per minute.Part How much time, in minutes, do water tank A and water tank B have to be drained in order for them to have the same amount of water?
Is 1 greater than 1?
Out of the 800 students enrolled in a recreationalflag-football program, 32% are seventh graders.How many students in the program are seventhgraders?sum1 helpppp ASAPPPPPPPP
Renee has a triangular garden with an area of 24 square feet. Which drawing shows Renee's garden?3 ft.6 ft.6ft.
In the first quadrant you start at (6, 10) and move 6 units right and 4 units down what point will you end up with

The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best reate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 10 Southwest flights and observing whether they arrive on time. (a) Find the probability that at least 3 flights arrive late.

Answers

Answer:

There is a 32.22% probability that at least 3 flights arrive late.

Step-by-step explanation:

For each flight, there are only two possible outcomes. Either it arrives on time, or it arrives late. This means that we can solve this problem using binomial probability concepts.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_(n,x).\pi^(x).(1-\pi)^(n-x)$

In which $C_(n,x)$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_(n,x) = (n!)/(x!(n-x)!)$

And $\pi$ is the probability of X happening.

In this problem, we have that:

There are 10 flights, so $n = 10$ .

A success in this case is a flight being late. 80% of its flights arriving on time, so 100%-80% = 20% arrive late. This means that $\pi = 0.2$ .

(a) Find the probability that at least 3 flights arrive late.

Either less than 3 flights arrive late, or at least 3 arrive late. The sum of these probabilities is decimal 1. This means that:

$P(X < 3) + P(X \geq 3) = 1$

$P(X \geq 3) = 1 - P(X < 3)$

In which

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = x) = C_(n,x).\pi^(x).(1-\pi)^(n-x)$

$P(X = 0) = C_(10,0).(0.2)^(0).(0.8)^(10) = 0.1074$

$P(X = 1) = C_(10,1).(0.2)^(1).(0.8)^(9) = 0.2684$

$P(X = 2) = C_(10,2).(0.2)^(2).(0.8)^(8) = 0.3020$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1074 + 0.2684 + 0.3020 = 0.6778$

Finally

$P(X \geq 3) = 1 - P(X < 3) = 1 - 0.6778 = 0.3222$

There is a 32.22% probability that at least 3 flights arrive late.

Final answer:

The problem is solved by calculating the probability of the complementary event (0,1,2 flights arriving late) using the binomial distribution, then subtracting this from 1 to find the probability of at least 3 flights arriving late.

Explanation:

This problem is typically solved by using a binomial probability formula, which is used when there are exactly two mutually exclusive outcomes of a trial, often referred to as 'success' and 'failure'.
Here, our 'success' is a flight arriving late. The probability of success, denoted as p, is thus 20% or 0.2 (since 80% arrive on time, then 100%-80% = 20% arrive late). The number of trials, denoted as n, is 10 (the number of randomly selected flights).
We want to find the probability that at least 3 flights arrive late, in other words, 3,4,...,10 flights arrive late. The problem can be solved easier by considering the complementary event: 0,1,2 flights arrive late. Then subtract the sum of these probabilities from 1.

The binomial probability of exactly k successes in n trials is given by:

P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))
Where C(n, k) is the binomial coefficient, meaning choosing k successes from n trials.
We calculate like so:
P(X=0) = C(10, 0) * (0.2)^0 * (0.8)^10
P(X=1) = C(10, 1) * (0.2)^1 * (0.8)^9
P(X=2) = C(10, 2) * (0.2)^2 * (0.8)^8
Sum these up and subtract from 1 to get the probability that at least 3 flights arrive late. This gives the solution to the question.

Learn more about binomial probability here:

brainly.com/question/34083389

#SPJ3

What is the relationship between 0.04 and 0.004?

Answers

I think the answer is that both are fractions whose denominators are powers of ten. 0.04 is 4 out of 100 and 0.004 is 4 out of 1000

C^3+64=

Help me understand this please.

Answers

the answer is 1000064 i dont know how to explain it

Arc Length and Radians question- please help! Will mark brainliest! Is 20pts!The answer is shown but please give me an explanation so I can show my work!

Answers

Answer:

Step-by-step explanation:

If we convert from degrees into radians, we can use the formula

$s=r\theta$ , where s is the arc length, r is the radius and θ is the angle in radians.

To convert from degrees to radians, we multiply by $(\pi)/(180)$

So $(140 \pi)/(180)$ is our angle in radians, and we have the radius - we can now plug in these two values into our equation.

$s=24*(140 \pi)/(180) =58.64$

Answer:

Step-by-step explanation:

length of arc= (arc angle/360) * 2πr

length= 140/360 *2*22/7*24

length=58.88 feet ~59 feet(approx)

Answers

Answer:

i know its a bit late but the answer below

Step-by-step explanation:

e/f

Could u be more specific

Please help me i will mark brainliest

Answers

Answer:

see below

Step-by-step explanation:

The cube of something to the 1/3 power is the original something. The cube of a cube root of something is the original something. Since the cube of a cube root is the same as the cube of a 1/3 power, the 1/3 power is equivalent to the cube root.

The applicable rules of exponents are ...

(a^b)^c = a^(bc)

Other Questions

Another rock in Death Valley at the Racetrack traveled 55.3 meters during the observation period of nine years. a . What was the rock's average speed in feet per year? Round your answer to the nearest whole number. feet per year b . If a strong wind gives a stone an initial velocity of v 0 = 11 m / s , and the friction coefficient of stone on ice is μ = 0.14 , and g = 9.81 m / s 2 . Use the equation v 2 0 = 2 μ g S to find the stopping distance S for the stone. Round your answer to the nearest tenth.

candy box is made from a piece of cardboard that measures 45 by 24 inches. Squares of equal size will be cut out of each comer. The sides will then be folded up to form a rectangular box. What size square should be cut from each corner to obtain maximum volume? inches should be cut away from each corner to obtain the maximum volume. A square with a side of length (Round to the nearest hundredth as needed.)

The grapThe graph below represents the distance Manuel walks over several hours.Which is an ordered pair on the line?(2.5, 14)(2.5, 14)(1.25, 5)(1.25, 5)(2.25, 12)(2.25, 12)(1.5, 9)

Suppose that X is a random variable with probability function x 0 1 2 3 4 5 P(x) 0.00032 0.0064 0.0512 0.2048 0.4096 0.32768 and that the random variable Y = 9X2 − 36X + 4. (a) What is the range of Y ? (b) Calculate P{Y = 4}. (c) Calculate P{Y = 0}.