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Trig Identities and Applications

Trig Identities and Applications. A calc student upset as could be That his antiderivative didn't agree With the one in the book E'en aft one more look. Oh! Seems he forgot to write the "+ C". . Objective. To integrate trig functions To write position, velocity, and acceleration functions.

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Trig Identities and Applications

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  1. Trig Identities and Applications A calc student upset as could be That his antiderivative didn't agree With the one in the book E'en aft one more look. Oh! Seems he forgot to write the "+ C".

  2. Objective • To integrate trig functions • To write position, velocity, and acceleration functions

  3. 4.1 Trig Identities and applications • What are the derivatives of… • sin x • cos x • tan x • sec x • csc x • cot x

  4. Trig identities

  5. Examples

  6. Words that mean integration… • Anti-derivative • Integral • General solution of a differential equation • Area under the curve • Position function

  7. Applications… solving for C • Given: f’(x)=2, f(3)=5 • Find: f(x)

  8. You try… • Given: f’(x) = x^2, f(2)=0. • Find f(x) • Given: f’’(x) = x, f’(0)=4, f(0)=2. • Find f(x)

  9. Position, velocity, and acceleration funcitons s(t) v(t) a(t)

  10. Ex 8, pg 247 • A ball is thrown upward with an initial velocity of 64 ft/sec from an initial height of 80 feet. • a) What is the position function?

  11. Ex 3…. • A ball is thrown upward with an initial velocity of 64 ft/sec from an initial height of 80 feet. • b) When does the ball hit the ground?

  12. Problem 63, pg 250 • A baseball is thrown upward from ground level with a velocity of 10 m/sec. What is it’s maximum height?

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