Please help!! will give brainly :)

If sinA+cosecA=3 find the value of sin2A+cosec2A

Irina18 [472]

Answer:

$\sin 2A + \csc 2A = 2.122$

Step-by-step explanation:

Let $f(A) = \sin A + \csc A$ , we proceed to transform the expression into an equivalent form of sines and cosines by means of the following trigonometrical identity:

$\csc A = \frac{1}{\sin A}$ (1)

$\sin^{2}A +\cos^{2}A = 1$ (2)

Now we perform the operations: $f(A) = 3$

$\sin A + \csc A = 3$

$\sin A + \frac{1}{\sin A} = 3$

$\sin ^{2}A + 1 = 3\cdot \sin A$

$\sin^{2}A -3\cdot \sin A +1 = 0$ (3)

By the quadratic formula, we find the following solutions:

$\sin A_{1} \approx 2.618$ and $\sin A_{2} \approx 0.382$

Since sine is a bounded function between -1 and 1, the only solution that is mathematically reasonable is:

$\sin A \approx 0.382$

By means of inverse trigonometrical function, we get the value associate of the function in sexagesimal degrees:

$A \approx 22.457^{\circ}$

Then, the values of the cosine associated with that angle is:

$\cos A \approx 0.924$

Now, we have that $f(A) = \sin 2A +\csc2A$ , we proceed to transform the expression into an equivalent form with sines and cosines. The following trignometrical identities are used:

$\sin 2A = 2\cdot \sin A\cdot \cos A$ (4)

$\csc 2A = \frac{1}{\sin 2A}$ (5)

$f(A) = \sin 2A + \csc 2A$

$f(A) = \sin 2A + \frac{1}{\sin 2A}$

$f(A) = \frac{\sin^{2} 2A+1}{\sin 2A}$

$f(A) = \frac{4\cdot \sin^{2}A\cdot \cos^{2}A+1}{2\cdot \sin A \cdot \cos A}$

If we know that $\sin A \approx 0.382$ and $\cos A \approx 0.924$ , then the value of the function is:

$f(A) = \frac{4\cdot (0.382)^{2}\cdot (0.924)^{2}+1}{2\cdot (0.382)\cdot (0.924)}$

$f(A) = 2.122$

8 0

3 years ago

Consider the arithmetic sequence:

prisoha [69]

Answer:

<em>Answer: D</em>

Step-by-step explanation:

<u>Arithmetic Sequences </u>

The arithmetic sequences are those where any term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.

The equation to calculate the nth term of an arithmetic sequence is:

$a_n=a_1+(n-1)r$

Where

an = nth term

a1 = first term

r = common difference

n = number of the term

We are given the arithmetic sequence:

10, 12, 14, 16, ...

Where a1=10 and

r = 12 - 10 = 2

Thus the general term is:

$a_n=10+(n-1)2$

Operating:

$a_n=10+2n-2$

$a_n=8+2n$

Answer: D

4 0

3 years ago

Read 2 more answers

What's the perimeter or how do you find it?

ziro4ka [17]

The perimeter of inside of the track is 536.44m

<h3>Perimeter of a circle and rectangle</h3>

The perimeter of a circle is also known as the circumference of the circle. The formula for calculating the circumference is expressed as:

C = 2πr

where

r is the radius

From the given diagram

r = 46/2 = 23m

C = 2(3.14)(23)
C = 144.44m

Find the perimeter of the rectangle

P = 2(l+w)

p = 2(46+150)
P = 2(196)
P =392m

The perimeter of the inside track = 144.44 + 392

The perimeter of the inside track = 536.44m

Hence the perimeter of inside of the track is 536.44m

Learn more on perimeter of composite shape here: brainly.com/question/16247505

#SPJ1

7 0

2 years ago

XPF is congruent to which correctly named triangle

guapka [62]

Answer:

the answer is triangle GBL

7 0

3 years ago

What type of number is 1/2?

makkiz [27]

Answer:

1/2 is a rational number.

Step-by-step explanation:

Real numbers are numbers that can represent "distance" along a line. The set of real numbers has subsets that include natural numbers, whole numbers, integers, and rational numbers.

Natural numbers are counting numbers. A.K.A., they are numbers that you would start counting your fingers on (1, 2, 3, ...)

Whole numbers are just natural numbers and 0.

Integers are whole numbers and their opposite. (..., -3, -2, -1, 0, 1, 2, 3, ...)

Rational numbers are integers and numbers that can be put into a fraction of two integers. For example, 3/4 is a fraction of two natural numbers (3 and 4) who are also integers. Therefore, 3/4 is a rational number.

So, what number is 1/2?

It can't be a natural number because no one counts numbers as fractions unless they were made to.

It can't be a whole number because 1/2 is not whole. It is half of 1.

It can't be an integer because integers include whole numbers and their opposites, and 1/2 isn't even a whole number.

1/2 has to be an rational number because it is a fraction of two integers, 1 and 2.

8 0

3 years ago