91Ó°ÊÓ

Find the exact value of the trigonometric expression given that \(\sin u=-\frac{7}{25}\) and \(\cos v=-\frac{4}{5} .\) (Both \(u\) and \(v\) are in Quadrant III.) $$\sin (u+v)$$

Rewrite the expression so that it is not in fractional form. There is more than one correct form of each answer. $$\frac{\sin ^{2} y}{1-\cos y}$$

Use the product-to-sum formulas to rewrite the product as a sum or difference. $$\sin 5 \theta \sin 3 \theta$$

Find the exact value of the trigonometric expression given that \(\sin u=-\frac{7}{25}\) and \(\cos v=-\frac{4}{5} .\) (Both \(u\) and \(v\) are in Quadrant III.) $$\tan (u-v)$$

Two ships leave a port at 9 A.M. One travels at a bearing of \(\mathrm{N} 53^{\circ} \mathrm{W}\) at 12 miles per hour, and the other travels at a bearing of \(\mathrm{S} 67^{\circ} \mathrm{W}\) at 16 miles per hour. Approximate how far apart they are at noon that day.

verify the identity. $$\tan \left(\sin ^{-1} \frac{x-1}{4}\right)=\frac{x-1}{\sqrt{16-(x-1)^{2}}}$$

Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval \([0,2 \pi)\). $$2 \sin x+\cos x=0$$

Rewrite the expression so that it is not in fractional form. There is more than one correct form of each answer. $$\frac{5}{\tan x+\sec x}$$

Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval \([0,2 \pi)\). $$4 \sin ^{3} x+2 \sin ^{2} x-2 \sin x-1=0$$

Find the exact value of the trigonometric expression given that \(\sin u=-\frac{7}{25}\) and \(\cos v=-\frac{4}{5} .\) (Both \(u\) and \(v\) are in Quadrant III.) $$\cot (v-u)$$