Question

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?

Answer 1

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
so,
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.