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

4.1 Trig Identities and applications

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

Trig identities

dxx2sec

dxxx tansec

dxx2csc

dxxx cotcsc

dxxsin

dxxcos

Examples

dxxsin2

dxxx )

cossin( 2

Words that mean integration…

Anti-derivative Integral General solution of a differential

equation Area under the curve Position function

Applications… solving for C

Given: f’(x)=2, f(3)=5 Find: f(x)

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)

Position, velocity, and acceleration funcitons

s(t)

v(t)

a(t)

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?

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?

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?