trig identities and applications
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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?