Posted by **Yul** on Monday, November 14, 2011 at 12:23am.

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 -
**Steve**, Tuesday, November 15, 2011 at 12:34am
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.

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