Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Trigonometric Functions - differentiation - Tangents, normals and other.
Test Yourself 1.


 

Solve the following problems - leave your answer in exact form unless otherwise indicated:

Tangents 1. Find the equation of the tangent to the curve y = sin 3x
at .
Answer.y = -3x + π.		 2. Find the equation of the tangent to y = sec x at .
  3. Find the equation of the tangent to y = 3 sin 2x + x - 2 at . 4. A curve has the equation

y = x cos x

Given that P is the first point to the right of the origin where the curve crosses the x axis, find the equation of the tangent
at point P.
  5. Find the equation of the tangent to y = 3 cosecx + 1 at . 6. Find the equation to
y = sinx + cos x at .
Answer.y = √2.
Normals 7. Find the equation of the normal
to the curve y = sin 2x
at the point (π/2, 0).
 8. Develop the equation of the normal to the curve y = x sin x
where x = π/2.
Answer.y = -x + π.
  9. Find the equation of the normal to y = 2 sin 2x + 3 at the point where . 10. (i) Find the equation of the normal to y = e cosx at x = π.

(ii) Determine the length of the normal to the curve from the point on the curve where x = π to the point where the normal crosses the x axis.

  11. Prove that the normal to y = x tan x at cuts the x axis at approximately x = 2.8. 12. Find the x values of the points on y = 3cosx + √2 (x) where the normal has a gradient which is undefined is the domain [0, π].
Answer.