SOLUTION: If (theta) is in the third quadrant and sin(theta)=-(3/5), what is cos(1/2 theta)? Give your answer as a fraction in simplest from. -half angle formulas

Algebra ->  Trigonometry-basics -> SOLUTION: If (theta) is in the third quadrant and sin(theta)=-(3/5), what is cos(1/2 theta)? Give your answer as a fraction in simplest from. -half angle formulas      Log On


   

Question 998930: If (theta) is in the third quadrant and sin(theta)=-(3/5), what is cos(1/2 theta)? Give your answer as a fraction in simplest from.
-half angle formulas
Answer by ikleyn(52908) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.  First calculate

     cos%28theta%29 = sqrt%281+-+sin%5E2%28theta%29%29 = sqrt%281+-+%28-3%2F5%29%5E2%29 = sqrt%28%2825-9%29%2F25%29 = sqrt%2816%2F25%29 = -4%2F5.

     The sign is "minus" because the angle   theta   is in the third quadrant.

2.  Next,   cos%28%281%2F2%29theta%29 = sqrt%28%281+%2B+cos%5E2%28theta%29%29%2F2%29.

     See the lesson  Trigonometric functions of half argument  in this site.

     It gives   cos%28%281%2F2%29theta%29 = -sqrt%28%281+%2B+cos%5E2%28theta%29%29%2F2%29 = -sqrt%28%281+%2B+%28-4%2F5%29%5E2%29%2F2%29 = -sqrt%28%2825+%2B+16%29%2F%282%2A25%29%29 = -sqrt%2841%2F50%29.

     The sign is  "minus"  because the angle   alpha%2F2   lies in the second quadrant.