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7-1 Basic Trig Identities

7-1 Basic Trig Identities. Identity- an equation for which all values will be true. For example, x = x is an identity because every number you plug in is true. Another way to look at it is one portion of the equation can replace the other. For example,

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7-1 Basic Trig Identities

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  1. 7-1 Basic Trig Identities

  2. Identity- an equation for which all values will be true. For example, x = x is an identity because every number you plug in is true. Another way to look at it is one portion of the equation can replace the other. For example, Tan = is an identity. Can’t you use the terms interchangeably?

  3. Reciprocal Identities: (yes, you need to know these!)

  4. Quotient identities

  5. Pythagorean Identities http://www.youtube.com/watch?v=RA6E_Ml42l4 sin2θ + cos2θ = 1 tan2θ + 1 = sec2θ cot2θ + 1 = csc2θ

  6. Examples: • If sec θ=3/2, find cosθ 2) If cscθ =4/3, find tanθ

  7. symmetric identities Sin(x+360k) = sin(x) (also works with cosine) Sin(x+180k) = -sinx if k=odd (Since the values of sine and cosine repeat every 360°)

  8. Examples: Find: Sin(600°) Cos(750◦)

  9. Opposite angle identities sin(-θ) = -sin(θ) cos(-θ) = cos(θ)

  10. Simplify Sinx +sinxcot2x

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