Unit 11 Review

Why does an identity proof need a common domain?

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State the defining idea behind identities, equations, and proof strategy in one precise sentence.

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For identities, equations, and proof strategy, what condition or domain restriction must remain visible in the solution?

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For identities, equations, and proof strategy, describe the most likely incorrect first step and explain why it fails.

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For identities, equations, and proof strategy, explain how this lesson's idea will be used later in the course.

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State the defining idea behind reciprocal, quotient, and pythagorean identities in one precise sentence.

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For reciprocal, quotient, and pythagorean identities, what condition or domain restriction must remain visible in the solution?

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For reciprocal, quotient, and pythagorean identities, describe the most likely incorrect first step and explain why it fails.

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For reciprocal, quotient, and pythagorean identities, explain how this lesson's idea will be used later in the course.

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Verify sin$$\frac{x}{1-cos x}=\frac{1+cos x}{sin} x$$

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For verifying identities strategically, what condition or domain restriction must remain visible in the solution?

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For verifying identities strategically, describe the most likely incorrect first step and explain why it fails.

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For verifying identities strategically, explain how this lesson's idea will be used later in the course.

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Find sin $15$ degrees exactly.

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State the defining idea behind sum and difference formulas in one precise sentence.

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For sum and difference formulas, describe the most likely incorrect first step and explain why it fails.

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For sum and difference formulas, explain how this lesson's idea will be used later in the course.

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Rewrite cos $2x$ entirely in terms of sin $x$.

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State the defining idea behind double-angle formulas in one precise sentence.

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For double-angle formulas, what condition or domain restriction must remain visible in the solution?

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For double-angle formulas, explain how this lesson's idea will be used later in the course.

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Find $cos(\frac{pi}{8})$ exactly.

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State the defining idea behind half-angle and power-reduction formulas in one precise sentence.

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For half-angle and power-reduction formulas, what condition or domain restriction must remain visible in the solution?

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For half-angle and power-reduction formulas, describe the most likely incorrect first step and explain why it fails.

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Rewrite sin $8x-sin 2x$ as a product.

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State the defining idea behind product-to-sum and sum-to-product formulas in one precise sentence.

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For product-to-sum and sum-to-product formulas, what condition or domain restriction must remain visible in the solution?

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For product-to-sum and sum-to-product formulas, describe the most likely incorrect first step and explain why it fails.

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For product-to-sum and sum-to-product formulas, explain how this lesson's idea will be used later in the course.

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State the defining idea behind equations using fundamental identities in one precise sentence.

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For equations using fundamental identities, what condition or domain restriction must remain visible in the solution?

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For equations using fundamental identities, describe the most likely incorrect first step and explain why it fails.

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For equations using fundamental identities, explain how this lesson's idea will be used later in the course.

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Solve $2cos^2 x+cos x-1=0$ on $[0,2pi)$.

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For quadratic-form trigonometric equations, what condition or domain restriction must remain visible in the solution?

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For quadratic-form trigonometric equations, describe the most likely incorrect first step and explain why it fails.

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For quadratic-form trigonometric equations, explain how this lesson's idea will be used later in the course.

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Solve $cos(2x)=0$ on $[0,2pi)$.

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State the defining idea behind multiple-angle equations in one precise sentence.

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For multiple-angle equations, describe the most likely incorrect first step and explain why it fails.

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For multiple-angle equations, explain how this lesson's idea will be used later in the course.

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Write all solutions to tan $x=-sqrt(3)$.

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State the defining idea behind general solutions and interval restrictions in one precise sentence.

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For general solutions and interval restrictions, what condition or domain restriction must remain visible in the solution?

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For general solutions and interval restrictions, explain how this lesson's idea will be used later in the course.

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What evidence should accompany a reported root $x\approx 0.739085$ of cos $x=x$?

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State the defining idea behind exact and numerical trigonometric equation solving in one precise sentence.

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For exact and numerical trigonometric equation solving, what condition or domain restriction must remain visible in the solution?

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For exact and numerical trigonometric equation solving, describe the most likely incorrect first step and explain why it fails.

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