Calculating Curve Tangent at x=-π/4

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SUMMARY

The discussion focuses on calculating the tangent line of the curve defined by the function f(x) = 1/3sin(3x - π/4) at the point x = -π/4. The derivative at this point is f'(-π/4) = -1, leading to the tangent line equation y = -1 * (x + π/4) + m. The correct y-value at x = -π/4 is determined to be approximately 0.79, indicating that the user initially miscalculated the sine value due to potential calculator mode errors. The conversation highlights the importance of using the correct mode for trigonometric calculations and suggests that derivative-related questions should be directed to the appropriate forum section.

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  • Proficiency in using graphing calculators or software in radian mode
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  • Learn about the properties of sine and cosine functions
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SwedishFred
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Homework Statement


Deside curve tangent in point x=-π/4


Homework Equations


f(x)=1/3sin(3x-π/4)
y=f(x)


The Attempt at a Solution


f`(-π/4)=-1
using the tangent equation
y=kx+m
y=-1*(-π/4)+m
y=1/3sin(3(-π/4)-π/4)
≈3.33*10^-14
3.33*10^-14=-1*(-π/4)+m
f(x)≈-1*(-π/4)+0,79
is this right ? I have a bad feeling...
 
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SwedishFred said:

Homework Statement


Deside curve tangent in point x=-π/4
Deside?
What is that?
Is the problem to find the line that is tangent to the curve at x = -π/4?
SwedishFred said:

Homework Equations


f(x)=1/3sin(3x-π/4)
y=f(x)


The Attempt at a Solution


f`(-π/4)=-1
using the tangent equation
y=kx+m
y=-1*(-π/4)+m
y=1/3sin(3(-π/4)-π/4)
≈3.33*10^-14
No.
When x = -π/4, y = 1/3 * sin(3(-π/4)-π/4)) = 1/3 * sin(-π). This is one of the angles whose sine and cosine you should have committed to memory. It looks like you might be using a calculator to do this, and either have the calculator in the wrong mode (it should be in radian mode) or you are using an approximation to π. Either way will not give you the right answer.

SwedishFred said:
3.33*10^-14=-1*(-π/4)+m
f(x)≈-1*(-π/4)+0,79
is this right ? I have a bad feeling...
 
By the way, questions that involve taking derivatives should be posted in the Calculus & Beyond section, not in the Precalculus section.
 

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