Finding the derivative of this trig function

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SUMMARY

The discussion centers on finding the derivative of the trigonometric function f(θ) = √3.cos²(θ) + sin(2θ) at θ = π/6. Participants clarify the question's translation and emphasize the need to compute the derivative f'(θ) and evaluate it at the specified angle. The derivative will provide the slope of the tangent line to the curve at that point, which is the crux of the homework problem presented.

PREREQUISITES
  • Understanding of trigonometric functions and their derivatives
  • Knowledge of calculus, specifically differentiation techniques
  • Familiarity with evaluating functions at specific points
  • Basic translation skills for mathematical terminology between languages
NEXT STEPS
  • Learn how to differentiate trigonometric functions, focusing on derivatives of sin(θ) and cos(θ)
  • Study the application of the chain rule in calculus
  • Practice evaluating derivatives at specific angles, particularly common angles like π/6
  • Explore the concept of tangent lines and their slopes in relation to curves
USEFUL FOR

Students studying calculus, particularly those focusing on trigonometric functions and their derivatives, as well as educators looking for examples of derivative applications in real-world problems.

leticia beira
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Homework Statement
homework
Relevant Equations
--
Para f (θ) = √3.cos² (θ) + sen (2θ), uma inclinação da reta tangente, uma função em θ = π / 6, é?
 
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leticia beira said:
Homework Statement:: homework
Relevant Equations:: --

For f (θ) = √3.cos² (θ) + sen (2θ), a slope of the tangent line, a function at θ = π / 6, is it?
Your attachments are not working for some reason. It looks like it might be a file security issue. What format are the files that you are trying to attach?
 
berkeman said:
Your attachments are not working for some reason. It looks like it might be a file security issue. What format are the files that you are trying to attach?
I don't think there is an attachment, other than possibly the translation from Portuguese to English.
I see post #1 in Portuguese, but the quoted text in post #2 is in English.

A better translation is, I believe, the following:
If ##f(\theta) = \sqrt 3 \cos^2(\theta) + \sin(\theta)##, find the slope of the tangent to the curve when ##\theta = \frac \pi 6##.​

@leticia beira, have you tried taking the derivative, ##f'(\theta)## and evaluating it at ##\theta = \frac \pi 6##? That seems to be what the question is asking for.
 
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