Michael D.

asked • 05/21/16# Pre 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: a

5

169 = c

√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: a

^{2}+b^{2}=c^{2}5

_{2}+12^{2}=c^{2}169 = c

^{2}√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 degreesThe 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

## Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.

Most questions answered within 4 hours.

#### OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.

Andrew M.

^{2}+b^{2}=c^{2}^{2}+12^{2}=c^{2}^{2}05/22/16