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Novay_Z [31]
3 years ago
5

Express sin(3theta) in terms of sin (theta)

Mathematics
2 answers:
BigorU [14]3 years ago
7 0
3∅ can be rewritten as (2∅+∅)
sin(3∅) = sin(2∅ + ∅<span>)
Opening brackets on the right hand side;
 = sin2</span>∅ cos ∅ + cos2∅sin<span>∅
</span><span>This simplifies to;
 = 2sin</span>∅cos^2∅ + sin∅ (1- 2sin^2∅<span>)
 = sin</span>∅ (2cos^2∅ + 1 - 2sin^2∅<span>)
 = sin</span>∅ (2(1 - sin^2∅) +1-2sin^2∅<span>)
 = 3sin</span>∅ - 4sin^3<span>∅</span>
tamaranim1 [39]3 years ago
5 0

First of all:-

3∅ can be called (2∅+∅)
so, sin(3∅) = sin(2∅ + ∅<span>)
Open brackets on the RHS (right hand side)
 = sin2</span>∅ cos ∅ + cos2∅sin<span>∅
</span><span>This is simplified into;
 = 2sin</span>∅cos^2∅ + sin∅ (1- 2sin^2∅<span>)
 = sin</span>∅ (2cos^2∅ + 1 - 2sin^2∅<span>)
 = sin</span>∅ (2(1 - sin^2∅) +1-2sin^2∅<span>)
 = 3sin</span>∅ - 4sin^3∅

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Tomtit [17]

Answer:

The answer is 364. There are 364 ways of choosing a recorder, a facilitator and a questioner froma club containing 14 members.

This is a Combination problem.  

Combination is a branch of mathematics that deals with the problem relating to the number of iterations which allows one to select a sample of elements which we can term "<em>r</em>" from a collection or a group of distinct objects which we can name "<em>n</em>". The rules here are that replacements are not allowed and sample elements may be chosen in any order.

Step-by-step explanation:

Step I

The formula is given as

C (n,r) = \frac{n}{r} = \frac{n!}{(r!(n-r)!)}

n (objects) = 14

r (sample) = 3

Step 2 - Insert Figures

C (14, 3) = (\frac{14}{3}) = \frac{14!}{(3!(14-3)!)}

= \frac{87178291200}{(6 X 39916800)}

= \frac{87178291200}{239500800}

= 364

Step 3

The total number of ways a recorder, a facilitator and a questioner can be chosen in a club containing 14 members therefore is 364.

Cheers!

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