Inverse Trig Functions & Derivatives of Trig Functions

Inverse Trig Functions & Derivatives of Trig Functions

Cole Zmurchok Math 102 Section 106

November 28, 2016

Today...

1. More Trig Function Derivatives 2. Inverse Trig Functions 3. Related Rates with Trig Functions

Course Evaluations: do these for all of your courses! Let me know if you need the website. WW 12 due Thursday Final Exam: Dec 12, 8:30 am

Warm-up

Q1. What is the period, T , of h(t) = 8 - 6 sin(4t)? A. T = 4 B. T = 1/4 C. T = 1 D. T = 2 E. T = /2

Warm-up

Q2. What is the amplitude of h(t) = 8 - 6 sin(4t)? A. 14 B. 8 C. 12 D. 6 E. -6

Warm-up

Q3. What is the derivative of tan(ex2)? A. sec2(ex2) B. sec2(ex2)ex2 C. sec2(ex2)ex2x2 D. sec2(ex2)ex22x E. sec2(ex2)ex2x22x

Derivatives of Trigonometric Functions

We already know that

d dx

sin

x

=

cos

x

d dx

cos

x

=

-

sin

x

We used the quotient rule to find

d

d

tan x =

sin x = sec2 x

dx

dx cos x

Derivatives of Trigonometric Functions

What is the derivative of cot(x)?

d

d cos x

cot x =

dx

dx sin x

- sin x sin x - cos x cos x

=

sin2 x

-1 = sin2 x

= - csc2 x

Inverse Trigonometric Functions

f (x) = sin x Inverse Trfig-o1n(oxm)e=tricafrucnscintio(nxs) "the angle whose sine is x"

1

x

1-x2

Figure 1T4.1h0e. Tahbiosvtreiatnrgialenhgalsebiesencocnonssttrruucctteeddsosothatht atis an angle wh 1 = x. This msienans =thaxt = arcsin(x)

This means that = arcsin x

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download