###### Asked in Trigonometry

Trigonometry

# Cos series expression?

## Answer

###### Wiki User

###### March 23, 2014 4:00PM

cos(x) = 1 - x2/2! + x4/4! - x6/6! + ... where x is the angle measured in radians.

## Related Questions

###### Asked in Math and Arithmetic, Trigonometry

### What is sin23A minus sin7A upon sin2A plus sin14A if A equals pi upon 21?

Using the identity, sin(X)+sin(Y) =
2*sin[(x+y)/2]*cos[(x-y)/2]
the expression becomes
{2*sin[(23A-7A)/2]*cos[(23A+7A)/2]}/{2*sin[(2A+14A)/2]*cos[(2A-14A)/2]}
= {2*sin(8A)*cos(15A)}/{2*sin(8A)*cos(-6A)}
= cos(15A)/cos(-6A)}
= cos(15A)/cos(6A)} since cos(-x) = cos(x)
When A = pi/21,
15A = 15*pi/21
and 6A = 6*pi/21 = pi - 15pi/21
Therefore, cos(6A) = - cos(15A)
and hence the expression = -1.

###### Asked in Calculus

### Simplify sinx cotx cosx?

== cot(x)== 1/tan(x) = cos(x)/sin(x)
Now substitute cos(x)/sin(x) into the expression, in place of
cot(x)
So now:
sin(x) cot(x) cos(x) = sin(x) cos(x) (cos(x)/sin(x) )
sin(x) cos(x) cos(x)/sin(x)
The two sin(x) cancel, leaving you with cos(x) cos(x)
Which is the same as cos2(x)
So:
sin(x) cot(x) cos(x) = cos2(x) ===

###### Asked in Math and Arithmetic, Calculus, Trigonometry

### What is the exact value of the expression cos 7pi over 12 cos pi over 6 -sin 7pi over 12 sin pi over 6?

cos(a)cos(b)-sin(a)sin(b)=cos(a+b)
a=7pi/12 and b=pi/6
a+b = 7pi/12 + pi/6 = 7pi/12 + 2pi/12 = 9pi/12
We want to find cos(9pi/12)
cos(9pi/12) = cos(3pi/4)
cos(3pi/4)= cos(pi-pi/4)
cos(pi)cos(pi/4)-sin(pi)sin(pi/4)
cos(pi)=-1
sin(pi)=0
cos(pi/4) = √2/2
sin(pi/4) =√2/2
cos(pi)cos(pi/4)-sin(pi)sin(pi/4) = - cos(pi/4) = -√2/2

###### Asked in Algebra, Trigonometry

### Use trigonometric identities to write each expression in terms of a single trigonometric function or a constant. simplify cos t sin t?

Thanks to the pre-existing addition and subtraction theorums, we
can establish the identity:
sin(a+b) = sin(a)cos(b)+sin(a)cos(b)
Then, solving this, we get
sin(a+b) = 2(sin(a)cos(b))
sin(a)cos(b) = sin(a+b)/2
a=b, so
sin(a)cos(a) = sin(a+a)/2
sin(a)cos(a) = sin(2a)/2
Therefore, the answer is sin(2a)/2.

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