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If f(theta) =| Cos^theta cos theta×sin theta -sin theta | |Cos theta×sin theta sin^2theta cos theta | |Sin theta -cos theta 0 | then value of f((2pi)/3) is?
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If f(theta) =| Cos^theta cos theta×sin theta -sin theta | |Cos theta×s...
Calculation of f((2pi)/3)
To calculate the value of f((2pi)/3), we need to substitute the value of theta as (2pi)/3 in the given expression.
Substituting theta as (2pi)/3
f((2pi)/3) = | Cos^((2pi)/3) cos((2pi)/3)×sin((2pi)/3) -sin((2pi)/3) | |Cos((2pi)/3)×sin((2pi)/3) sin^2((2pi)/3) cos((2pi)/3) | |Sin((2pi)/3) -cos((2pi)/3) 0 |
Simplifying the expression
Now, we can simplify the expression by using some trigonometric identities.
cos((2pi)/3) = -0.5
sin((2pi)/3) = sqrt(3)/2
sin^2((2pi)/3) = 3/4
cos((2pi)/3) = -0.5
sin((2pi)/3) = sqrt(3)/2
sin((2pi)/3) -cos((2pi)/3) = sqrt(3)/2 + 0.5
Substituting these values in the expression, we get:
f((2pi)/3) = |-0.5*(-0.5)*sqrt(3)/2 - sqrt(3)/2| |-0.5*sqrt(3)/2*3/4*(-0.5)| |sqrt(3)/2 + 0.5 0|
Simplifying further, we get:
f((2pi)/3) = |-3sqrt(3)/8 - sqrt(3)/2| |3sqrt(3)/16| |sqrt(3)/2 + 0.5 0|
f((2pi)/3) = |5sqrt(3)/8| |3sqrt(3)/16| |sqrt(3)/2 + 0.5 0|
Therefore, the value of f((2pi)/3) is 5sqrt(3)/8.
To calculate the value of f((2pi)/3), we need to substitute the value of theta as (2pi)/3 in the given expression.
Substituting theta as (2pi)/3
f((2pi)/3) = | Cos^((2pi)/3) cos((2pi)/3)×sin((2pi)/3) -sin((2pi)/3) | |Cos((2pi)/3)×sin((2pi)/3) sin^2((2pi)/3) cos((2pi)/3) | |Sin((2pi)/3) -cos((2pi)/3) 0 |
Simplifying the expression
Now, we can simplify the expression by using some trigonometric identities.
cos((2pi)/3) = -0.5
sin((2pi)/3) = sqrt(3)/2
sin^2((2pi)/3) = 3/4
cos((2pi)/3) = -0.5
sin((2pi)/3) = sqrt(3)/2
sin((2pi)/3) -cos((2pi)/3) = sqrt(3)/2 + 0.5
Substituting these values in the expression, we get:
f((2pi)/3) = |-0.5*(-0.5)*sqrt(3)/2 - sqrt(3)/2| |-0.5*sqrt(3)/2*3/4*(-0.5)| |sqrt(3)/2 + 0.5 0|
Simplifying further, we get:
f((2pi)/3) = |-3sqrt(3)/8 - sqrt(3)/2| |3sqrt(3)/16| |sqrt(3)/2 + 0.5 0|
f((2pi)/3) = |5sqrt(3)/8| |3sqrt(3)/16| |sqrt(3)/2 + 0.5 0|
Therefore, the value of f((2pi)/3) is 5sqrt(3)/8.
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If f(theta) =| Cos^theta cos theta×sin theta -sin theta | |Cos theta×sin theta sin^2theta cos theta | |Sin theta -cos theta 0 | then value of f((2pi)/3) is?
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