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cosθ =5/13 with -π/2 < θ <0 find each of the following

sin( θ - 5π/4)
cos( θ - 11π/6)
tan( θ + 5π/4)

can some1 explain to me how to do these? im completely lost and this is the only thing about my assignment that i cant do can someone please help me?

  • trig -

    Ah, finally a legible posting! :-)

    This is an exercise in the addition/subtraction formulas.

    First off, it is clear that θ is in the 4th quadrant, so
    sinθ = -12/13
    tanθ = -12/5

    sin(a-b) = sina cosb - cosa sinb
    sin(θ - 5π/4) = sinθ cos 5π/4 - cosθ sin 5π/4
    = (-12/13)(-1/√2) - (5/13)(-1/√2)
    = 17/(13√2)

    Do the others the same way, using the appropriate addition formula.

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