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Trigonometric Identities and Equations Homework Solutions

This homework assignment focuses on verifying and simplifying trigonometric identities, as well as solving various trigonometric equations. Key topics include sine and cosine sum and difference identities, double angle formulas, and inverse trigonometric functions. Solutions involve finding all angles for given equations over the specified periods and rewriting expressions using sine and cosine. Students are tasked with comprehending and applying fundamental concepts in trigonometry to enhance their problem-solving skills.

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Trigonometric Identities and Equations Homework Solutions

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  1. 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 cscx • #25 - #30 are all verifying problems

  2. 7.4 Trigonometric Identities Simplify/Verify an Expression Verify: • Simplify:

  3. 7.5 Sum and Difference Identities Sine Sum and Difference Sine and Cosine Double Angle sin (2Ɵ) = 2sin ƟcosƟ cos (2Ɵ) = cos2Ɵ – sin2Ɵ = 1 – 2sin2Ɵ = 2cos2Ɵ – 1 Rewrite the following only in terms of sin Ɵ and cosƟ:sin (2Ɵ) + cosƟ • For all angles α and β, sin (α+ β) =sin αcosβ + cosα sin βsin (α – β) = sin αcosβ – cosα sin β • Prove:sin (Ɵ + π/2) = cosƟ

  4. 7.5 Sum and Difference Identities Solve. cos(2x) + cosx = 0 2cos x + sin(2x) = 0

  5. 7.6 Solving Trig Equations and Inequalities Analytically Factoring Trig Equations Find all solutions in one period of:2tan2x = sec x – 1 • Find all solutions to 2sin2x – sin x = 1

  6. 7.2 Inverse Trigonometric Functions Graphing Inverse Trig Sinusoids Determine if the following are sinusoidal. If so, rewrite it as a sinusoid. • State the domain and range of each. Graph. • y = sin-1 (x) + 1 • y = cos-1 (2x) • y = 3sin-1 (2x) – 1

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