Pg. 407/423 Homework

• Pg. 407 #33Pg. 423 #16 – 18 all

• #19 Ѳ = kπ #21 t = 0.52 + 2kπ, 2.62 + 2kπ• #23 x = π/2 + 2kπ #25 x = π/6 + 2kπ, 5π/6 + 2kπ• #27 x = ±1.05 + 2kπ, π + 2kπ

• #10 csc x• #25 - #30 are all verifying problems

7.4 Trigonometric Identities

Simplify/Verify an Expression• Simplify: • Verify:1 tan

1 cot

sin cos cot csc

7.5 Sum and Difference Identities

Sine Sum and Difference• For all angles α and β,

sin (α + β) =sin α cos β + cos α sin β

sin (α – β) = sin α cos β – cos α sin β

• Prove:sin (Ɵ + π/2) = cos Ɵ

Sine and Cosine Double Angle• sin (2Ɵ) = 2sin Ɵ cos Ɵ• cos (2Ɵ) = cos2 Ɵ – sin2 Ɵ

= 1 – 2sin2 Ɵ = 2cos2 Ɵ – 1

• Rewrite the following only in terms of sin Ɵ and cos Ɵ:

sin (2Ɵ) + cos Ɵ

7.5 Sum and Difference Identities

Solve.2cos x + sin(2x) = 0 cos(2x) + cos x = 0

7.6 Solving Trig Equations and Inequalities Analytically

Factoring Trig Equations• Find all solutions to

2sin2 x – sin x = 1 • Find all solutions in one

period of:2tan2 x = sec x – 1

7.2 Inverse Trigonometric Functions

Graphing Inverse Trig• State the domain and range

of each. Graph.• y = sin-1 (x) + 1• y = cos-1 (2x)• y = 3sin-1 (2x) – 1

Sinusoids• Determine if the following

are sinusoidal. If so, rewrite it as a sinusoid.

2sin 3 1 5cos 3 2y x x

sin 3 1 3cos 2 2y x x

3sin 4 1 2cos 2 3y x x