Unit 11 Mastery Check

Why does an identity proof need a common domain?

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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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Simplify$$\frac{sec^2 x-1}{tan} x$$

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Simplify$$\frac{sec^2 x-1}{tan} x$$

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

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

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State the defining idea behind verifying identities strategically in one precise sentence.

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

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Find sin $15$ degrees exactly.

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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, what condition or domain restriction must remain visible in the solution?

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

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

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

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

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

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

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

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State the defining idea behind quadratic-form trigonometric equations in one precise sentence.

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

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