Question

Equations of tangent lines to trig functions calculator.

A) Tangent line solver
B) Trig tangent calculator
C) Tangent line to sine calculator
D) Trig function tangent line finder

Answer 1

To find the equation of a tangent line to a trigonometric function, you can use the derivative of the function. The correct answer is option A .

Step-by-step explanation:

To find the equation of a tangent line to a trigonometric function, you can use the derivative of the function. Let's take the example of finding the equation of a tangent line to the sine function, y = sin(x).

1. Take the derivative of the sine function, which is cos(x).
2. Select a point on the curve, for example, (0, sin(0)) = (0, 0).
3. Use the point-slope form of a line, y - y1 = m(x - x1), where m is the derivative and (x1, y1) is the point on the curve.
4. Substitute the values and simplify the equation to get the equation of the tangent line.

For the sine function, the equation of the tangent line at (0,0) would be y = x.

To find the equation of a tangent line to the sine function, one calculates the derivative to obtain the slope and applies the point-slope formula. Alternatively, a TI-83, 83+, or 84 calculator can be used to compute this efficiently. Understanding these processes is critical for trigonometry and geometry.