You're given a function f(x)=3tan(x) -4sin(x) +2cos(x). Find f(a) if: sin a=4/5 and pi/2 < a
I'm confused about what they're asking here, find f(a), do they mean find f(x) by replacing the given values in the function? Cause I can't see any alphas in the function.
If that would be the case then what do I have to replace in the expression? I'm only given sin a value?
Also I'm confused, what should I do with pi/2 < a
Thanks!
I'm confused about what they're asking here, find f(a), do they mean find f(x) by replacing the given values in the function? Cause I can't see any alphas in the function.
If that would be the case then what do I have to replace in the expression? I'm only given sin a value?
Also I'm confused, what should I do with pi/2 < a
Thanks!
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f(x) is a function of variable x
f(α) is a value of this function f(x) for a fixed number α
This fixed number α is defined by relations
sin(α) = 4/5
and
π/2 < α < π
From the above relations we have to find cos(α) and tan(α).
cos²(α) = 1 - sin²(α)
cos(α) = -√[1 - sin²(α)] = -√[1 - (4/5)²] = - 3/5
Note: The negative sign of the above cosine is because π/2 < α < π. This is where we needed this relation. For 0 < α < π/2 the cosine would be positive.
tan(α) = sin(α) / cos(α) = (4/5) / (- 3/5) = - 4/3
So we have the answer
f(α) = 3 tan(α) - 4 sin(α) + 2 cos(α) = 3 (- 4/3) - 4 (4/5) + 2 (- 3/5) = - 42/5 = - 8.4
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f(α) is a value of this function f(x) for a fixed number α
This fixed number α is defined by relations
sin(α) = 4/5
and
π/2 < α < π
From the above relations we have to find cos(α) and tan(α).
cos²(α) = 1 - sin²(α)
cos(α) = -√[1 - sin²(α)] = -√[1 - (4/5)²] = - 3/5
Note: The negative sign of the above cosine is because π/2 < α < π. This is where we needed this relation. For 0 < α < π/2 the cosine would be positive.
tan(α) = sin(α) / cos(α) = (4/5) / (- 3/5) = - 4/3
So we have the answer
f(α) = 3 tan(α) - 4 sin(α) + 2 cos(α) = 3 (- 4/3) - 4 (4/5) + 2 (- 3/5) = - 42/5 = - 8.4
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