SOLUTION: Use the given conditions to find the exact value of the expression. sin α = − 5/13, tan α > 0, sin(α − 2π/3) I am not sure if I need to solve for sin a=-5/13 or sin (

Algebra ->  Equations -> SOLUTION: Use the given conditions to find the exact value of the expression. sin α = − 5/13, tan α > 0, sin(α − 2π/3) I am not sure if I need to solve for sin a=-5/13 or sin (      Log On


   

Question 1158674: Use the given conditions to find the exact value of the expression.
sin α = − 5/13, tan α > 0, sin(α − 2π/3)
I am not sure if I need to solve for sin a=-5/13 or sin (a-2π/3)
Please help! I want to know how to do this problem so if you could walk me through it that would help a lot! Thank you.

Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
use the given conditions to find the exact value of the expression:
sin%28a%29=%28-5%2F13%29, tan%28a%29%3E+0, sin%28a-%282pi%2F3%29%29
Since sin%28a%29+=+-5%2F13 , and tan+%28a%29+%3E+0+, it follows that cos%28a%29+%3C+0 (Third quadrant)
So
cos+%28a%29+=-sqrt%28+1+-+%285%2F13%29%5E2+%29
cos+%28a%29+=+-sqrt%28%28169+-+25%29%2F169+%29
cos+%28a%29++=+-+12%2F13

so,
sin%28a-%282pi%2F3%29%29=sin%28a%29%2Acos%282pi%2F3%29-cos%28a%29%2Asin%282pi%2F3%29

Substituting values: sin%28a%29=%28-5%2F13%29,cos%282pi%2F3%29=-1%2F2, cos+%28a%29++=+-+12%2F13, sin%282pi%2F3%29=sqrt%283%29%2F2

sin%28a-%282pi%2F3%29%29=%28-5%2F13%29%28-1%2F2%29-%28-12%2F13%29%28sqrt%283%29%2F2%29

sin%28a-%282pi%2F3%29%29=%285%2F26%29%2B12+sqrt%283%29%2F26

sin%28a-%282pi%2F3%29%29=%285%2B12sqrt%283%29%29%2F26

sin%28a-%282pi%2F3%29%29=5%2F26+%2B+%286sqrt%283%29%29%2F13