AttachedASK060705Thanks! **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.**\[ \sin(u/2) = \_\_\_\_\_\_ \]\[ \cos(u/2) = \_\_\_\_\_\_ \]\[ \tan(u/2) = \_\_\_\_\_\_ \]---**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.

Name: AttachedASK060705Thanks! **Trigonometric Half-Angle Formulas Exercise*
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
Description: AttachedASK060705Thanks! **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- [ ] Q