SOLUTION: find the exact value of sin(a) knowing that tan a=2/5, and 𝜢∈𝐈𝐈𝐈𝐐.

Algebra ->  Trigonometry-basics -> SOLUTION: find the exact value of sin(a) knowing that tan a=2/5, and 𝜢∈𝐈𝐈𝐈𝐐.      Log On


   

Question 1177586: find the exact value of sin(a) knowing that tan a=2/5, and 𝜢∈𝐈𝐈𝐈𝐐.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


recall:
Sine Function:
sin%28a%29+=+Opposite+%2F+Hypotenuse
Cosine Function:
cos%28a%29+=+Adjacent+%2F+Hypotenuse
Tangent Function:
tan%28a%29+=+Opposite+%2F+Adjacent

given tan%28a%29=2%2F5 =>opp=2 and adj=5
find hypothenuse
hyp%5E2=opp%5E2%2Badj%5E2
hyp%5E2=2%5E2%2B5%5E2
hyp=sqrt%284%2B25%29
hyp=sqrt%2829%29

sin%28a%29=2%2Fsqrt%2829%29 or sin%28a%29=-2%2Fsqrt%2829%29

since given angle is in quadrant III , sin is negative, so use
sin%28a%29=-2%2Fsqrt%2829%29