What is cos(338)? Solve by hand, no calculator.
Correct answer gets BRAINLIEST.

9514 1404 393

  0.927184

Step-by-step explanation:

Assuming you want cos(338°), it is equal to cos(22°). This value is an irrational root of a 26th-degree polynomial. (Neither the polynomial, nor the root are easy to find by hand.)

The values of trig functions for 30° and 45° are well-known, as are half-angle and angle sum/difference formulas. The nearest angle for which cosine is relatively easy to find is 22.5°. A 2nd-order Maclaurin series expansion of the cosine function about that angle gives the approximation ...

  cos(x) ≈ cos(π/8)(1 -π²/128) +π/8·sin(π/8) +(π/8·cos(π/8) -sin(π/8))x -1/2·cos(π/8)x²

For your angle of 22°, the value of x needed in this expression is 11π/90. The values of cos(π/8) and sin(π/8) are the irrational numbers ...

  cos(π/8) = √(2 +√2)/2 ≈ 0.92387953

  sin(π/8) = √(2 -√2)/2 ≈ 0.38268343

If you use the approximation pi ≈ 355/113, both for the above formula and for the angle of interest, this reduces to the sum ...

  cos(22°) ≈ 71√(2-√2)/16272 +132383951√(2+√2)/264777984

This would be tedious to calculate by hand, but is not impossible. The value this sum produces will be correct when rounded to 7 decimal digits.

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Before calculators, trig function values were found in published tables. These days, tables are available on-line. Previously, they were published in books, usually along with information that helped with interpolation between table values, when necessary. The attachment shows a portion of an online cosine table suitable for answering your question.

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Additional comment

Before calculators, mathematicians spent lifetimes calculating accurate trig tables. For all but a very few angles, the cosine function of rational degree values will be an irrational number, as it is for cos(22°).

we'll this would mean that the dunk tank and the bounce house are the same for 20 hours because the 2 represents that the two activities, and the 20 represents the amount of hours they both are. so with this said, it means that the answer is c. the costs for a dunk tank and bounce house are the same for 20 hours.

c.the costs for a dunk tank and bounce house are the same for 20 hours.

hope this .

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d