SOLUTION: Can someone tell me if this is correct. Use definitions or identities to find the exact value of the 5 remaining trig functions. if sin = sqrt(2)/2 then: sin = sqrt(2)/2 t

Algebra ->  Trigonometry-basics -> SOLUTION: Can someone tell me if this is correct. Use definitions or identities to find the exact value of the 5 remaining trig functions. if sin = sqrt(2)/2 then: sin = sqrt(2)/2 t      Log On


   



Question 7102: Can someone tell me if this is correct. Use definitions or identities to find the exact value of the 5 remaining trig functions.
if sin = sqrt(2)/2
then:
sin = sqrt(2)/2
tan = 1
cosecant = 2/sqrt(2)
secant = 2/sqrt(2)
cotangent = 1
They just dont seem correct to me... Thanks for the help

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
One way to assure yourself that these are indeed correct is to draw a right triangle whose hypotenuse is length 2, and whose legs are each length sqrt%282%29 Since this is an isosceles triangle, the angles opposite the right angle are each 45 degrees. Call them angle A.
Remember: sohcahtoa ? (no, no, not the indian guide!) it's the acronym for remembering the trigonometric relationships with the sides of the right triangle. h = hypotenuse, o = side opposite, a = side adjacent.
In your triangle, h+=+2, o+=+sqrt%282%29 and a+=+sqrt%282%29
Sin = o/h
Cos = a/h
Tan = o/a
From this triangle, you can see that:
Sin+A+=+%28sqrt%282%29%29%2F2
Tan+A+=+%28sqrt%282%29%29%2Fsqrt%282%29 = 1
cosecant+A+=+2%2Fsqrt%282%29
secant+A+=+2%2Fsqrt%282%29
Cotangent+A+=+%28sqrt%282%29%29%2Fsqrt%282%29 = 1