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3 years ago

A parabola opens down if the value of is negative in the general form of the equation.

Mathematics

2 answers:

hammer [34]3 years ago

7 0

When a <0 Hope this helps :)

salantis [7]3 years ago

7 0

Answer:

The answer is the negative value of "a".

Step-by-step explanation:

In order to determine the answer, we have to know about the general form of the quadratic function.

The general form is:

$f(x)=ax^2+bx+c$

where a , b and c are real numbers and a not equal to zero.

I have attached an image that shows the general graph of the quadratic function. We can see that:

If the value of "a" is positive, the parabola opens up.
If the value of "a" is negative, the parabola opens down.

It depends on the coefficient next to the quadratic variable.

Finally, the negative value of "a" makes that the parabola opens down.

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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: