 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 44738 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.

Annual percentage yield (APY)
The rate that would give the same return if interest were computed just once a year

Continuous at x = a
lim x:a x a ƒ(x) = ƒ(a)

Divergence
A sequence or series diverges if it does not converge

Dot product
The number found when the corresponding components of two vectors are multiplied and then summed

Frequency (in statistics)
The number of individuals or observations with a certain characteristic.

Inverse cosecant function
The function y = csc1 x

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

Multiplication property of inequality
If u < v and c > 0, then uc < vc. If u < and c < 0, then uc > vc

Numerical derivative of ƒ at a
NDER f(a) = ƒ1a + 0.0012  ƒ1a  0.00120.002

Observational study
A process for gathering data from a subset of a population through current or past observations. This differs from an experiment in that no treatment is imposed.

Polynomial in x
An expression that can be written in the form an x n + an1x n1 + Á + a1x + a0, where n is a nonnegative integer, the coefficients are real numbers, and an ? 0. The degree of the polynomial is n, the leading coefficient is an, the leading term is anxn, and the constant term is a0. (The number 0 is the zero polynomial)

Present value of an annuity T
he net amount of your money put into an annuity.

Pythagorean
Theorem In a right triangle with sides a and b and hypotenuse c, c2 = a2 + b2

Real part of a complex number
See Complex number.

Rectangular coordinate system
See Cartesian coordinate system.

Reference triangle
For an angle ? in standard position, a reference triangle is a triangle formed by the terminal side of angle ?, the xaxis, and a perpendicular dropped from a point on the terminal side to the xaxis. The angle in a reference triangle at the origin is the reference angle

Window dimensions
The restrictions on x and y that specify a viewing window. See Viewing window.

Xscl
The scale of the tick marks on the xaxis in a viewing window.

zaxis
Usually the third dimension in Cartesian space.

zcoordinate
The directed distance from the xyplane to a point in space, or the third number in an ordered triple.