Use the given conditions. sin(u) = 25 7
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![**Trigonometric Half-Angle Formulas Exercise**
Use the given conditions.
\[ \sin(u) = \frac{7}{25}, \quad \frac{\pi}{2} < u < \pi \]
**(a) Determine the quadrant in which \( u/2 \) lies.**
- [ ] Quadrant I
- [ ] Quadrant II
- [ ] Quadrant III
- [ ] Quadrant IV
**(b) Find the exact values of \( \sin(u/2) \), \( \cos(u/2) \), and \( \tan(u/2) \) using the half-angle formulas.**
\[ \sin(u/2) = \_\_\_\_\_\_ \]
\[ \cos(u/2) = \_\_\_\_\_\_ \]
\[ \tan(u/2) = \_\_\_\_\_\_ \]
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**Explanation for Educators:**
This exercise involves applying half-angle identities in trigonometry. Here, the value of \( \sin(u) \) is given and it is specified that \( u \) is between \( \frac{\pi}{2} \) and \( \pi \). Students need to determine the quadrant where \( u/2 \) lies and then find the exact trigonometric values for \( \sin(u/2) \), \( \cos(u/2) \), and \( \tan(u/2) \).
**Half-Angle Formulas:**
\[ \sin\left(\frac{u}{2}\right) = \pm \sqrt{\frac{1 - \cos(u)}{2}} \]
\[ \cos\left(\frac{u}{2}\right) = \pm \sqrt{\frac{1 + \cos(u)}{2}} \]
\[ \tan\left(\frac{u}{2}\right) = \pm \sqrt{\frac{1 - \cos(u)}{1 + \cos(u)}} \]
The signs depend on the quadrant in which \( u/2 \) is located.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9fe49cee-acc8-403b-8d12-20ec3514f583%2F2658bcda-7ab3-4ef0-a1e6-f73a69f69bda%2Fym16td7_processed.png&w=3840&q=75)
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