
Michael D.
asked 05/21/16Pre Calculus
Use the given triangle to evaluate the trigonometric expression. The graph is a right triangle, the side on the y-axis =5 and the side o the x-axis =12. The hypotenuse is not given. sin(y/2)=?
a) 2/√3
b) 4/13
c) 6/13
d) √8/13
More
2 Answers By Expert Tutors

Norbert W. answered 07/09/16
Tutor
4.4
(5)
Math and Computer Language Tutor
There is another possibility, but there could be a misprint in the answer.
Let a = 5, be the length on the y- axis
Let b = 12, be the length on the x-axis
Again, the hypotenuse would be c = 13, by the Pythagorean Theorem.
Suppose y is the angle that is made between the y-axis and the hypotenuse.
From this, cos(y) = 5/13.
From the half-angle formula, sin(y/2) = √((1 - cos(y))/2)
With the given value of cos(y), sin(y/2) = 2/√13
This would answer a, if it was misprinted.
Without seeing the actually drawing, there might be a misprint in the question or the answers given above.

Andrew M. answered 05/22/16
Tutor
New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors
You have a right triangle with leg lengths of 5 and 12.
The hypotenuse will be 13.
This is from the Pythagorean Theorem: a2+b2=c2
52+122=c2
169 = c2
√169 = c
13 = c
However; since there is no picture here... I'm not sure
what your "y/2" signifies in sin(y/2) = ?
The hypotenuse will be 13.
This is from the Pythagorean Theorem: a2+b2=c2
52+122=c2
169 = c2
√169 = c
13 = c
However; since there is no picture here... I'm not sure
what your "y/2" signifies in sin(y/2) = ?
*******************************************
We can find the angles that are missing from the triangle.
We have a 90 degree angle ... The other 2 angles must
sum to 90 degrees.
Taking the horizontal line of length 12...
And using the hypotenuse length of 13
cos x = 12/13
Take inverse cosine of each side
x = cos-1(12/13) ≅ 22.62 degrees
The other angle will be 180 - (90+22.62) ≅ 67.38 degrees
That is the angle created between the vertical line up to (0,5)
and the hypotenuse running diagonally from there to (12,0)
If your problem is misprinted and is actually
[sin(y)]/2
sin(67.38)/2≅ .461538
and
6/13 ≅ .461538
I believe the answer you are looking for is c ... 6/13
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Andrew M.
05/22/16