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6.7

6.7. Trig Equations. Trig equations are equations involving trig functions that are satisfied by some values of the variable. The values that satisfy the equation are called the solutions of the equations. Ex. cos θ = ½

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6.7

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  1. 6.7 Trig Equations

  2. Trig equations are equations involving trig functions that are satisfied by some values of the variable. The values that satisfy the equation are called the solutions of the equations. Ex. cos θ = ½ The θ’s between 0 and 2π are π/3 and 5π/3, however we want all answers, so we get θ = π/3 + 2πk and θ = 5π/3 + 2πk Where k is any integer.

  3. Ex. 2 2 sin θ + √3 = 0, 0 ≤ θ ≤ 2π Get sin by itself sin θ = - √3 /2 What θ’s have sin equal to - √3 /2? θ = 4π/3 and 5π/3

  4. Ex. 3 tan (θ – π/2) = 1, 0 ≤ θ ≤ 2π We know that tan (π/4) = 1 so θ – π/2 = π/4 + kπ , k any integer (?) Now solve for θ, we get θ = 3π/4 + kπ In our interval θ = 3π/4 and 7π/4

  5. Trig equations use everything that you have learned: trig values, inverse trig, ASTC, identities and trig functions. HW pg 511 1-18 all Due weds

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