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Sever21 [200]
3 years ago
8

Find the exact value of the following expression (without using a calculator): tan(Sin^-1 x/2)

Mathematics
1 answer:
makvit [3.9K]3 years ago
7 0

ANSWER

\tan(\sin^{ - 1}( \frac{x}{2} ))  =  \frac{x}{ \sqrt{4 -  {x}^{2} } }  \:  \:where \:  \: x \ne \pm2

EXPLANATION

We want to find the exact value of

\tan( \sin^{ - 1}( \frac{x}{2}  ) )

Let

y = \sin^{ - 1}( \frac{x}{2} )

This implies that

\sin(y) =  \frac{x}{2}

This implies that,

The opposite is x units and the hypotenuse is 2 units.

The adjacent side is found using Pythagoras Theorem.

{a}^{2}  +  {x}^{2}  =  {2}^{2}

{a}^{2}  +  {x}^{2}  =  4

{a}^{2} = 4 - {x}^{2}

a=  \sqrt{4 - {x}^{2}}

This implies that,

\tan(y)  =  \frac{opposite}{adjacent}

\tan(y)  =  \frac{x}{ \sqrt{4 -  {x}^{2} } }

But

y = \sin^{ - 1}( \frac{x}{2} )

This implies that,

\tan(\sin^{ - 1}( \frac{x}{2} ))  =  \frac{x}{ \sqrt{4 -  {x}^{2} } }  \:  \:where \:  \: x \ne \pm2

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Answer:

Step-by-step explanation:

3.AE = CE                   E is the midpoint of AC

4. ∠AEB = ∠CED        Vertically opposite angles are equal

5. ΔAEB = ΔCED       ASA congruence

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3 years ago
he length of a rectangle is three times the width. The perimeter is 240 inches. Find the length and the width.
sammy [17]

Answer:

Length = 90 inch.

width = 30 inch

Let width of the rectangle = x inch.

So the length = 3x inch.

Perimeter = 2(length + width) = 2 (3x + x) = 8x.

So,

length = 3x = 3(30) = 90 inch.

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Describe in words the similarities and differences in multiplying and dividing complex numbers.
iragen [17]

Answer:

t does not matter if the two numbers are the same for multiplication or division. 4. ( ÷ ) To divide two fractions, take the second fraction, and flip it so that the top number is now on the bottom and vice versa, then multiply the two fractions together like you would for number 3.

Step-by-step explanation:

7 0
4 years ago
The charge for electricity consumption E is partly constant and partly varies as the number N of units used. The charge for 82 u
balandron [24]

The charge per unit of electricity is #415

The formula for E in terms of N is E = 375 + 40N

<h3>What is variation?</h3>

Variation is a mathematical term that establishes the relationship between quantities and variables in an equation.

Analysis:

E = K + CN

where K and C are constants

When E = 3655, N = 82 and when E = 2055, N = 42

3655 = K + 82C ---------------1

2055 = K + 42C----------------2

subtract equation 2 from 1

40C = 1600

C = 40

substitute C in equation 1

3655 = K + 82(40)

3655 = K + 3280

K = 3655 - 3280 = 375

charge per unit is N = 1

E = 375 + 40(1) = #415

Formula for E in terms of N is E = 375 + 40N

In conclusion, the charge per unit of electricity is 415 and the equation connecting E and N is E = 375 + 40N

Learn more about Variation: brainly.com/question/6499629

SPJ1

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2 years ago
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