SOLUTION: If tan x=20/21, and, pi < x < 3pi/2 what is sin (x+pi/2) Enter your answer as a fraction in simplest form, like this: 3/14

Algebra ->  Trigonometry-basics -> SOLUTION: If tan x=20/21, and, pi < x < 3pi/2 what is sin (x+pi/2) Enter your answer as a fraction in simplest form, like this: 3/14      Log On


   



Question 1092900: If tan x=20/21, and, pi < x < 3pi/2 what is sin (x+pi/2)
Enter your answer as a fraction in simplest form, like this: 3/14

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Note that +x+ is in the 3rd quadrant, so actually
+tan%28x%29+=+%28-20%29%2F%28-21%29+
+%28-20%29%2F%28-21%29+=+20%2F21+
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The length of the rotating vector is:
+c+=+sqrt%28+20%5E2+%2B+21%5E2+%29+
+c+=+sqrt%28+400+%2B+441+%29+
+c+=+sqrt%28+841+%29+
+c+=+29+
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Since a general rule is: +sin%28+x+%2B+pi%2F2+%29+=+cos%28+x+%29+
+cos%28+x+%29+=+-21%2F29+
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Note that if +pi+%3C+x+%3C+3pi%2F2+, then
+x+%2B+pi%2F2+ is an angle in the 4th quadrant
where the sin function is negative