STUDY GUIDE, CHAPTER 11
11.1:
Simplify a trig
expression. Example: 
Expect to use
reciprocal, ratio and/or Pythagorean identities; maybe add fractions or use a
conjugate.
11.2 Use identities to find the exact value of the sine, cosine or tangent of an angle that is a multiple of 15o, or I may give it to you in radians as a multiple of π/12.
Ex: cos (5π/12), sin(75o)
11.2 Use
the sum or difference identities to simplify expressions like
sin(π−x), cos(π/3+x), tan(x−3π/2)
11.3 Use
double- or half-angle identities for the sine or cosine (no calculator)
Example Given that sin θ = −5 / 6 and cos
θ = − sqrt(11) / 6,
(a)
which quadrant is θ in?
(b)
based on (a), which two quadrants could the angle 2θ be in?
(c)
use double-angle identities to find sin(2θ) and cos(2θ) without a
calculator.
(d)
based on (d), which quadrant must the angle 2θ be in? Is this consistent with (b)?
(e)
based on (a), which quadrant must the angle θ/2 be in?
(f) use the
quadrant from part (c) to determine the signs of sin(θ/2) and
cos(θ/2)
(g)
use half-angle identities to find sin(θ/2) and cos(θ/2) without a
calculator;
choose
the signs based on part (f).
11.4 Find
the exact functional value, without a calculator, of expressions like tan−1(sqrt(3)/3):
(Exercises
1-13; for the negatives: you must know the restricted domains)
11.5 Solve
for all solutions for a trig equation graphically, using a calculator;
or,
solve for all solutions between 0 and 2π (0o and 360o):
Examples
6, 7; exercises 25, 29, 33, 37, 39, 41
11.5A Solve
for all solutions of a trig equation without a calculator, for angles having
exact values;
or,
solve for all solutions between 0 and 2π (0o and 360o):
Examples
1, 2; Exercises 1, 3, 5, 17, 29
Return to: Merced College; Don Power Updated 11/28/05 by Don Power