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.

## Answer this Question

## Related Questions

- Precalc/Trig - Sorry there are quite a few problems, but I just need to know if ...
- trigonometry - given tanθ= -2√10/3 and π/2<θ< π ...
- trigonometry - tanθ= -2sqrt10/3 and π/2<θ< π find a. ...
- math - given sinθ=-5/13 and π<θ<3π/2 find sin2θ ...
- trigonometry - if cosθ=2/3 and tanθ<0 find the exact value sin(&#...
- math - if cosθ=2/3 and tanθ<0 find the exact value sin(θ-5&#...
- mathematics - given sinθ=-5/13 and π<θ<3π/2 find sin2...
- TRIGONOMETRY - Can you check my work, please? This is for a trig study guide for...
- Math - Calculus - The identity below is significant because it relates 3 ...
- Trig - The set of solution(s) of 2 cos^2 (θ) - 13 cos(θ) + 6 = 0 that ...