Trig Identities and Applications

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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".

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Objective

• To integrate trig functions
• To write position, velocity, and acceleration
  functions

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4.1 Trig Identities and applications

• What are the derivatives of
• sin x
• cos x
• tan x
• sec x
• csc x
• cot x

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Trig identities
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Examples
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Words that mean integration

• Anti-derivative
• Integral
• General solution of a differential equation
• Area under the curve
• Position function

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Applications solving for C

• Given f(x)2, f(3)5
• Find f(x)

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You try

• Given f(x) x2, f(2)0.
• Find f(x)
• Given f(x) x, f(0)4, f(0)2.
• Find f(x)

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

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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?

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Problem 63, pg 250

• A baseball is thrown upward from ground level
  with a velocity of 10 m/sec. What is its
  maximum height?

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