SOLUTION: Find the exact values for Sin(theta), Cos(theta), Tan(theta). using the information given.. Sin(2theta) = 24/25; 2theta in QII. I have tried using a Double Angle Identity for

Algebra ->  Trigonometry-basics -> SOLUTION: Find the exact values for Sin(theta), Cos(theta), Tan(theta). using the information given.. Sin(2theta) = 24/25; 2theta in QII. I have tried using a Double Angle Identity for      Log On


   

Question 1099273: Find the exact values for Sin(theta), Cos(theta), Tan(theta). using the information given..
Sin(2theta) = 24/25; 2theta in QII.
I have tried using a Double Angle Identity for Sine, Cosine, and Tangent but I am not anywhere near the answer, I am confused on exactly what I should do..
Thanks in advance.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Using the projections of +25+ = rotaing vector
+b%5E2+=+c%5E2+-+a%5E2+ ( projection on the horizontal axis )
+b%5E2+=+25%5E2+-+24%5E2+
+b%5E2+=+625+-+576+
+b%5E2+=+49+
+b+=+-7+
( negative because +2theta+ is in 2nd quadrant )
---------------------------------------------
The angle theta will be in the 1st quadrant where all
trig functions are positive
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I'll use 1/2 angle formulas
+sin%28+%282theta%29%2F2%29+=+sqrt%28+%28+1+-+cos%282theta%29+%29+%2F+2+%29+
+sin%28+theta+%29+=+sqrt%28+%28+1+-+%28-7%2F25%29+%29+%2F+2+%29+
+sin%28+theta+%29+=+sqrt%28%28+25%2F25+%2B+7%2F25+%29+%2F+2+%29+
+sin%28+theta+%29+=+sqrt%28+%28+32%2F25+%29%2F2+%29+
+sin%28+theta+%29+=+sqrt%28+16%2F25+%29+
+sin%28+theta+%29+=+4%2F5+ ( sin is positive in 1st quadrant )
---------------------------------------------------
+cos%28+theta+%29+=+sqrt%28%28+1+%2B+cos%28+2theta+%29+%29%2F2+%29+

+cos%28+theta+%29+=+sqrt%28+9%2F25+%29+
+cos%28+theta+%29+=+3%2F5+ ( cos is positive in 1st quadrant )
------------------------------
+tan%28+theta+%29+=+%281+-+cos%28+2theta+%29%29+%2F+sin%28+2theta+%29+
The answer should be +4%2F3+ You can finish