Tangent Line to f(x) Without Specified Point

Click For Summary
SUMMARY

The discussion focuses on finding the equation of the tangent line to the function f(x) = -sin²(x) + 1/2 within the interval [0, π/2], which makes an angle of 135° with the x-axis. The user initially misinterprets the angle's corresponding x-coordinate as 3π/4, which is outside the specified interval. The correct approach involves determining the slope of the tangent line using the angle and finding an appropriate point within the defined range to calculate the tangent line's equation.

PREREQUISITES
  • Understanding of trigonometric functions and their properties
  • Knowledge of calculus, specifically derivatives and tangent lines
  • Familiarity with the unit circle and angle measures
  • Ability to solve equations involving sine and cosine functions
NEXT STEPS
  • Learn how to calculate derivatives of trigonometric functions
  • Study the concept of tangent lines and their equations
  • Explore the unit circle and its application in determining angles
  • Investigate the relationship between angles and slopes in coordinate geometry
USEFUL FOR

Students studying calculus, particularly those learning about tangent lines and trigonometric functions, as well as educators seeking to clarify concepts related to angles and derivatives.

johnstobbart
Messages
22
Reaction score
0

Homework Statement



Hello again.

The question asks me to find an equation of the tangent to the graph:

f(x)= - sin^2 x + 1/2, x \epsilon [0, \frac{\pi}{2}

which makes an angle of 135° with the x-axis (measure anti-clockwise from the positive x-axis). Assume that the scales along the x- and y- axis are the same.

I just don't know how to find the point.

Homework Equations





The Attempt at a Solution



What I did was took the 135° value from the unit circle, which I think is:
\frax{3\pi}{4}
and worked with that as my x-coordinate.

The problem is that the question states that x ε [0, ∏/2], which means that 3∏/4 can't be x.

The only other value I can think of getting is:
√2/2 from sin(2∏ - 3∏/4).

What am I overlooking?
 
Physics news on Phys.org

Similar threads

Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 13 ·
Replies
13
Views
3K
Replies
1
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
Replies
2
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
13
Views
5K