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7.1.1 Trig Identities and Uses

7.1.1 Trig Identities and Uses. We have already discussed a few example of trig identities All identities are meant to serve as examples of equality Convert one expression into another Can be used to verify relationships or simplify expressions in terms of a single trig function or similar.

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7.1.1 Trig Identities and Uses

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  1. 7.1.1 Trig Identities and Uses

  2. We have already discussed a few example of trig identities • All identities are meant to serve as examples of equality • Convert one expression into another • Can be used to verify relationships or simplify expressions in terms of a single trig function or similar

  3. Past Identities • Past identities we have already talked about include: • 1) Reciprocal Identities • 2) Quotient identities (tan, cot) • 3) Cofunction identities

  4. Period Identities • Recall, the period of a trig function is how often/over how many radians the values for the trig function repeat • sin(x + 2π) = sin(x) • cos(x + 2π) = cos(x) • tan(x + π) = tan(x) • csc(x + 2π) = csc(x) • sec(x + 2π) = sec(x) • cot(x + π) = cot(x)

  5. Odd/Even • Looking at the values of particular functions on the unit circle reveals some other information • Odd: f(-x) = -f(x) • Opposite x yields opposite y-value • Even: f(-x) = f(x) • Opposite x yields the same y-value

  6. Odd/Even • sin(-x) = -sin(x) csc(-x) = -csc(x) • cos(-x) = cos(x) sec(-x) = sec(x) • tan(-x) = -tan(x) cot(-x) = -cot(x)

  7. Pythagorean Identities • We can let x = cos(x) and y = sin(x) in terms of x/y coordinates on the coordinate grid • The same may apply to triangles

  8. Our end goal is to with a simpler form of a long, entirely winded, expression • Most times, we will need to use more than one trig identity to help us

  9. Example. Simplify the expression: • cos(x) + sin(x) tan(x)

  10. Example. Simplify the expression: • sec(x) cot(x) – cot(x) cos(x)

  11. Example. Simplify the expression: • sin2(x) – cos2(x)sin2(x)

  12. Assignment • Pg.553 • # 1-7

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