 3.6.1: Determine the sign (+ or ) that yields the correct formula for the ...
 3.6.2: Which of the following functions can be differentiated using the ru...
 3.6.3: Compute d dx (sin2 x + cos2 x) without using the derivative formula...
 3.6.4: How is the addition formula used in deriving the formula (sin x) = ...
 3.6.5: In Exercises 524, compute the derivative. f (x) = sin x cos x
 3.6.6: In Exercises 524, compute the derivative. f (x) = x2 cos x
 3.6.7: In Exercises 524, compute the derivative. f (x) = sin2 x
 3.6.8: In Exercises 524, compute the derivative. f (x) = 9 sec x + 12 cot x
 3.6.9: In Exercises 524, compute the derivative. H (t) = sin t sec2 t
 3.6.10: In Exercises 524, compute the derivative. h(t) = 9 csc t + t cot t
 3.6.11: In Exercises 524, compute the derivative. f ( ) = tan sec
 3.6.12: In Exercises 524, compute the derivative. k( ) = 2 sin2
 3.6.13: In Exercises 524, compute the derivative. f (x) = (2x4 4x1)sec x
 3.6.14: In Exercises 524, compute the derivative. f (z) = z tan z
 3.6.15: In Exercises 524, compute the derivative. y = sec
 3.6.16: In Exercises 524, compute the derivative. G(z) = 1 tan z cot z
 3.6.17: In Exercises 524, compute the derivative. R(y) = 3 cos y 4 sin y
 3.6.18: In Exercises 524, compute the derivative. f (x) = x sin x + 2
 3.6.19: In Exercises 524, compute the derivative. f (x) = 1 + tan x 1 tan x
 3.6.20: In Exercises 524, compute the derivative. f ( ) = tan sec
 3.6.21: In Exercises 524, compute the derivative. f (x) = ex sin x
 3.6.22: In Exercises 524, compute the derivative. h(t) = et csc t
 3.6.23: In Exercises 524, compute the derivative. f ( ) = e (5 sin 4 tan )
 3.6.24: In Exercises 524, compute the derivative. f (x) = xex cos x
 3.6.25: In Exercises 2534, find an equation of the tangent line at the poin...
 3.6.26: In Exercises 2534, find an equation of the tangent line at the poin...
 3.6.27: In Exercises 2534, find an equation of the tangent line at the poin...
 3.6.28: In Exercises 2534, find an equation of the tangent line at the poin...
 3.6.29: In Exercises 2534, find an equation of the tangent line at the poin...
 3.6.30: In Exercises 2534, find an equation of the tangent line at the poin...
 3.6.31: In Exercises 2534, find an equation of the tangent line at the poin...
 3.6.32: In Exercises 2534, find an equation of the tangent line at the poin...
 3.6.33: In Exercises 2534, find an equation of the tangent line at the poin...
 3.6.34: In Exercises 2534, find an equation of the tangent line at the poin...
 3.6.35: In Exercises 3537, use Theorem 1 to verify the formula. d dx cot x ...
 3.6.36: In Exercises 3537, use Theorem 1 to verify the formula. d dx sec x ...
 3.6.37: In Exercises 3537, use Theorem 1 to verify the formula. d dx csc x ...
 3.6.38: Show that both y = sin x and y = cos x satisfy y = y. I
 3.6.39: In Exercises 3942, calculate the higher derivative. f ( ), f ( ) = ...
 3.6.40: In Exercises 3942, calculate the higher derivative. d2 dt2 cos2 t
 3.6.41: In Exercises 3942, calculate the higher derivative. y, y, y = tan x...
 3.6.42: In Exercises 3942, calculate the higher derivative. y, y, y = et si...
 3.6.43: Calculate the first five derivatives of f (x) = cos x. Then determi...
 3.6.44: Find y(157), where y = sin x.
 3.6.45: Find the values of x between 0 and 2 where the tangent line to the ...
 3.6.46: Plot the graph f ( ) = sec + csc over [0, 2] and determine the numb...
 3.6.47: Let g(t) = t sin t. (a) Plot the graph of g with a graphing utility...
 3.6.48: Let f (x) = (sin x)/x for x = 0 and f (0) = 1. (a) Plot f on [3, 3]...
 3.6.49: Show that no tangent line to the graph of f (x) = tan x has zero sl...
 3.6.50: The height at time t (in seconds) of a mass, oscillating at the end...
 3.6.51: The horizontal range R of a projectile launched from ground level a...
 3.6.52: Show that if 2 <<, then the distance along the xaxis between and t...
 3.6.53: Use the limit definition of the derivative and the addition law for...
 3.6.54: Use the addition formula for the tangent tan(x + h) = tan x + tan h...
 3.6.55: Verify the following identity and use it to give another proof of t...
 3.6.56: Show that a nonzero polynomial function y = f (x) cannot satisfy th...
 3.6.57: Let f (x) = x sin x and g(x) = x cos x. (a) Show that f (x) = g(x) ...
 3.6.58: Figure 5 shows the geometry behind the derivative formula (sin ) = ...
Solutions for Chapter 3.6: Trigonometric Functions
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 3.6: Trigonometric Functions
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3. This expansive textbook survival guide covers the following chapters and their solutions. Since 58 problems in chapter 3.6: Trigonometric Functions have been answered, more than 24503 students have viewed full stepbystep solutions from this chapter. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885. Chapter 3.6: Trigonometric Functions includes 58 full stepbystep solutions.

Characteristic polynomial of a square matrix A
det(xIn  A), where A is an n x n matrix

Combinatorics
A branch of mathematics related to determining the number of elements of a set or the number of ways objects can be arranged or combined

Compound fraction
A fractional expression in which the numerator or denominator may contain fractions

DMS measure
The measure of an angle in degrees, minutes, and seconds

Double inequality
A statement that describes a bounded interval, such as 3 ? x < 5

Ellipse
The set of all points in the plane such that the sum of the distances from a pair of fixed points (the foci) is a constant

Exponential decay function
Decay modeled by ƒ(x) = a ? bx, a > 0 with 0 < b < 1.

Halfangle identity
Identity involving a trigonometric function of u/2.

Infinite limit
A special case of a limit that does not exist.

Magnitude of an arrow
The magnitude of PQ is the distance between P and Q

Measure of center
A measure of the typical, middle, or average value for a data set

Measure of spread
A measure that tells how widely distributed data are.

Multiplicity
The multiplicity of a zero c of a polynomial ƒ(x) of degree n > 0 is the number of times the factor (x  c) (x  z 2) Á (x  z n)

Open interval
An interval that does not include its endpoints.

Period
See Periodic function.

Reflection across the xaxis
x, y and (x,y) are reflections of each other across the xaxis.

Root of an equation
A solution.

Stretch of factor c
A transformation of a graph obtained by multiplying all the xcoordinates (horizontal stretch) by the constant 1/c, or all of the ycoordinates (vertical stretch) of the points by a constant c, c, > 1.

Tree diagram
A visualization of the Multiplication Principle of Probability.

Whole numbers
The numbers 0, 1, 2, 3, ... .