SOLUTION: If sec(A) = \sqrt(65), and A is in Quadrant 1, find Sin2A and SinA/2.

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Question 1155697: If sec(A) = \sqrt(65), and A is in Quadrant 1, find Sin2A and SinA/2.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

If sec%28A%29+=+sqrt%2865%29, and A is in Quadrant 1,
find sin%282A%29 and sin%28A%2F2%29

use identity:
sec+%28A%29=1%2Fcos%28A%29

cos%28A%29=1%2Fsec%28A%29......plug in given

cos%28A%29=1%2Fsqrt%2865%29

use identity:
sin%5E2%28A%29%2Bcos%5E2%28A%29=1

sin%5E2%28A%29=1-cos%5E2%28A%29..........cos%5E2%28A%29=%281%2Fsqrt%2865%29%29%5E2=1%2F65

sin%5E2%28A%29=1-1%2F65

sin%5E2%28A%29=64%2F65

sin%28A%29=sqrt%2864%2F65%29

sin%28A%29=sqrt%2864%29%2Fsqrt%2865%29

sin%28A%29=8%2Fsqrt%2865%29

use identity:
sin%282A%29+=2sin%28A%29%2Acos%28A%29

sin%282A%29+=2%288%2Fsqrt%2865%29%29%2A%281%2Fsqrt%2865%29%29

sin%282A%29+=16%2F%28sqrt%2865%29%2Asqrt%2865%29%29

sin%282A%29+=16%2F65

use identity:
sin%28A%2F2%29=2+sin%28A%2F4%29+%2Acos%28A%2F4%29

sin%28A%2F2%29=2%28%288%2Fsqrt%2865%29%29%2F4%29%2A%28%281%2Fsqrt%2865%29%29%2F4%29

sin%28A%2F2%29=2%282%2Fsqrt%2865%29%29%2A%281%2F%284sqrt%2865%29%29%29

sin%28A%2F2%29=+%284%2Fsqrt%2865%29%29%2A%281%2F%284sqrt%2865%29%29%29

sin%28A%2F2%29=+1%2F65