PRECALC

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solve the equation

1. cos(θ) − sin(θ) = 1

2.2 cos(θ) tan(θ) + tan(θ) = 1 + 2 cos(θ)


3. sin(θ) cos(3θ) + cos(θ) sin(3θ) = 0


4. sin(2θ) cos(θ) − cos(2θ) sin(θ) = 1/2


5. cos(2θ) + cos(θ) = 2



6. cos(2θ) + sin2(θ) = 0

  • PRECALC -

    #1, look how I did this similar problem, and follow the same steps

    http://www.jiskha.com/display.cgi?id=1461697741

    #2
    2 cos(θ) tan(θ) + tan(θ) = 1 + 2 cos(θ)
    2cosθtanθ - 2cos + tanθ - 1 = 0
    2cosθ(tanθ - 1) + (tanθ -1) = 0
    by grouping:
    (tan - 1)(2cosθ + 1) = 0
    tanθ = 1 or cosθ = -1/2
    θ = 45 or θ = 225 or θ = 240 or θ =300 degrees
    in radians: θ = π/4, 5π/4, 4π/3, 5π/3

    #3 and #4 are based on the formula
    sin(A ± B) = sinAcosB ± cosAsinB

    I will do #4, you do #3
    sin(2θ) cos(θ) − cos(2θ) sin(θ) = 1/2
    sin(2θ - θ) = 1/2
    sin θ = 1/2
    θ = 30 degrees or θ = 150 degrees
    or θ = pi/6 or 5pi/6

    #5
    I will assume you mean:
    cos(2θ) + sin^2 (θ) = 0
    cos^2 θ - sin^2 θ + sin^2 θ = 0
    cos^2 θ = 0
    cosθ = 0
    θ = 90 or θ = 270 degrees
    θ = pi/2 or 3pi/2

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