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True [87]
3 years ago
5

Tan(2 sin^-1 0.4) Find the Exact value

Mathematics
1 answer:
stiv31 [10]3 years ago
7 0

Answer:

tan(2u)=[4sqrt(21)]/[17]

Step-by-step explanation:

Let u=arcsin(0.4)

tan(2u)=sin(2u)/cos(2u)

tan(2u)=[2sin(u)cos(u)]/[cos^2(u)-sin^2(u)]

If u=arcsin(0.4), then sin(u)=0.4

By the Pythagorean Identity, cos^2(u)+sin^2(u)=1, we have cos^2(u)=1-sin^2(u)=1-(0.4)^2=1-0.16=0.84.

This also implies cos(u)=sqrt(0.84) since cosine is positive.

Plug in values:

tan(2u)=[2(0.4)(sqrt(0.84)]/[0.84-0.16]

tan(2u)=[2(0.4)(sqrt(0.84)]/[0.68]

tan(2u)=[(0.4)(sqrt(0.84)]/[0.34]

tan(2u)=[(40)(sqrt(0.84)]/[34]

tan(2u)=[(20)(sqrt(0.84)]/[17]

Note:

0.84=0.04(21)

So the principal square root of 0.04 is 0.2

Sqrt(0.84)=0.2sqrt(21).

tan(2u)=[(20)(0.2)(sqrt(21)]/[17]

tan(2u)=[(20)(2)sqrt(21)]/[170]

tan(2u)=[(2)(2)sqrt(21)]/[17]

tan(2u)=[4sqrt(21)]/[17]

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irrelevant information in the first paragraph.

The ONLY information you need is:

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That's ALL .

(You don't even need to know that the bus has 55 seats.
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_________________________

If the people on the trip are going to share the cost of the bus,
then the cost of each share depends on the number of people.

             Less people ==> each one pays more.
             More people ==> each one pays less.

Just like everybody in the office sharing the cost of
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#6 and #7 should really be done in the reverse order ...
do #7 before you worry about #6.
Before you can fill in the table in #6, you absolutely need
to have the equation, whether or not you realize it.

The total cost is fixed . . . It's $780 .

If 2 people go on the trip, each one pays  780 / 2 .
If 3 people go on the trip, each one pays  780 / 3 .
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If 5 people go on the trip, each one pays  780 / 5 .
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<span>  #7).             P  =  780 / n .

</span>Now, filling in the table in #6 is a piece 'o cake.<span>

</span>5 people. . . . . . . 780 / 5
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Just don't go past 55 people.  The equation changes after that.

For ANY number of people, even hundreds, and ANY number
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