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Trigonometric Identities: Verification and Simplification

Solve trigonometric equations, verify identities, simplify expressions, and use sum and difference identities. Explore solving techniques and practice to master trigonometry concepts effectively.

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Trigonometric Identities: Verification and Simplification

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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: • Verify:

  3. 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

  4. 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 cosƟsin (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

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