91Ó°ÊÓ

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

Use the fundamental identities to simplify the expression. There is more than one correct form of each answer. $$\cot \left(\frac{\pi}{2}-x\right) \cos x$$

Use the fundamental identities to simplify the expression. There is more than one correct form of each answer. $$\frac{\cos ^{2} y}{1-\sin y}$$

(a) use a graphing utility to graph each side of the equation to determine whether the equation is an identity, (b) use the table feature of a graphing utility to determine whether the equation is an identity, and (c) confirm the results of parts (a) and (b) algebraically. $$\left(1+\cot ^{2} x\right)\left(\cos ^{2} x\right)=\cot ^{2} x$$

Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval \([0,2 \pi)\). $$x \tan x-1=0$$

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

Use the fundamental identities to simplify the expression. There is more than one correct form of each answer. $$\cos t\left(1+\tan ^{2} t\right)$$

A family is traveling due west on a road that passes a famous landmark. At a given time the bearing to the landmark is \(\mathrm{N} 62^{\circ} \mathrm{W},\) and after the family travels 5 miles farther the bearing is \(\mathrm{N} 38^{\circ} \mathrm{W}\). What is the closest the family will come to the landmark while on the road?

(a) use a graphing utility to graph each side of the equation to determine whether the equation is an identity, (b) use the table feature of a graphing utility to determine whether the equation is an identity, and (c) confirm the results of parts (a) and (b) algebraically. $$\csc x(\csc x-\sin x)+\frac{\sin x-\cos x}{\sin x}+\cot x=\csc ^{2} x$$

Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval \([0,2 \pi)\). $$x \cos x-1=0$$