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 |
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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. |
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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. |
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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. |