SOLUTION: Suppose sin(x) = 1/2 and tan(x) > 0. Find sin(x + 5π/6) and cos(x - 5π/3). sin(x + 5π/6) = cos(x - 5π/3) =

Algebra ->  Trigonometry-basics -> SOLUTION: Suppose sin(x) = 1/2 and tan(x) > 0. Find sin(x + 5π/6) and cos(x - 5π/3). sin(x + 5π/6) = cos(x - 5π/3) =      Log On


   

Question 923449: Suppose sin(x) = 1/2 and tan(x) > 0.
Find sin(x + 5π/6) and cos(x - 5π/3).
sin(x + 5π/6) =
cos(x - 5π/3) =
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose sin(x) = 1/2 and tan(x) > 0.
Find sin(x + 5π/6) and cos(x - 5π/3).
sin(x + 5π/6) =
cos(x - 5π/3) =
***
reference angle x is in quadrant I where sin>0, cos>0
use addition formulas for sin and cos
..
sinx=1/2 (working with a (30-60) reference right triangle in quadrant I)
cosx=√3/2
..
sin(x+5π/6) =sinxcos(5π/6)+cosxsin(5π/6)=1/2*-√3/2+√3/2*1/2=√3/4+√3/4=2√3/4=√3/2
..
cos(x-5π/3)=cosxcos(5π/6)-sinxsin(5π/6)=√3/2*-√3/2-1/2*1/2=3/4-1/4=1/2