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3 years ago

What is sin(4a) & cos(4a) if tan(a)=3

Mathematics

1 answer:

ratelena [41]3 years ago

6 0

Answer:

sin(4a) = -24/25
cos(4a) = 7/25

Step-by-step explanation:

Your calculator can tell you these values:

sin(4a) = sin(4·arctan(3)) = -0.96 = -24/25

cos(4a) = cos(4·arctan(3)) = 0.28 = 7/25

_____

Some useful trig identities are ...

sin(2a) = 2tan(a)/(1 +tan(a)^2)

cos(2a) = (1 -tan(a)^2)/(1 +tan(a)^2)

Filling in the given value for tan(a), we find ...

sin(2a) = 2(3)/(1+3^2) = 6/10 = 3/5

cos(2a) = (1 -3^2)/(1 +3^2) = -8/10 = -4/5

Now, double-angle formulas are useful:

sin(4a) = 2sin(2a)cos(2a) = 2(3/5)(-4/5) = -24/25

cos(4a) = 1 -2sin(2a)^2 = 1 -2(3/5)^2 = 7/25

The desired trig function values are sin(4a) = -24/25; cos(4a) = 7/25.

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Answer:

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Step-by-step explanation:

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probability of red marble= m/(n+m)

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Answer:

$y = 6\cdot z$

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$z$ - Number of times that Keith volunteered at pet shelter.

Step-by-step explanation:

After reading the statement of the problem, the following variables are described below:

$x$ - Number of times that Jason volunteered at pet shelter.

$y$ - Number of times that Noah volunteered at pet shelter.

$z$ - Number of times that Keith volunteered at pet shelter.

The following two relations are presented herein:

Noah and Jason

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Jason and Keith

$x = 2\cdot z$

The relationship between the number of times Noah and Keith volunteered is:

$y = 6\cdot z$

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