Chapter 8

Find each integral. $$ \int(\cos t-\sin t) d t $$

Differentiate each function. $$ f(t)=t^{3} \sin t $$

Find each integral. $$ \int(\sin t+\cos t) d t $$

Differentiate each function. $$ f(t)=t^{2} \cos t $$

Find each integral. $$ \int(1+\sin x) d x $$

Differentiate each function. $$ f(t)=\frac{\cos t}{t} $$

Find each integral. $$ \int(\cos x-1) d x $$

Differentiate each function. $$ f(t)=(1+\sin t)^{4} $$

Evaluate without using a calculator. a. \(\tan \frac{\pi}{6}\) b. \(\csc \frac{\pi}{6}\)

Differentiate each function. $$ f(t)=\sin \left(t^{3}+1\right) $$

Evaluate without using a calculator. a. \(\cot \frac{\pi}{6}\) b. \(\sec \frac{\pi}{6}\)

Find each integral. $$ \int t^{2} \sin \left(t^{3}+1\right) d t $$

Differentiate each function. $$ f(t)=\cos \left(t^{3}+t+1\right) $$

Evaluate without using a calculator. a. \(\tan \frac{3 \pi}{2}\) b. \(\csc \frac{3 \pi}{2}\)

Find each integral. $$ \int \sin \pi t d t $$

Differentiate each function. $$ f(t)=\sin 5 t $$

Evaluate without using a calculator. a. \(\cot \frac{3 \pi}{2}\) b. \(\sec \frac{3 \pi}{2}\)

Find each integral. $$ \int \cos 2 t d t $$

Differentiate each function. $$ f(t)=\cos 4 t $$

Evaluate without using a calculator. a. \(\tan \frac{3 \pi}{4}\) b. \(\sec \frac{3 \pi}{4}\)

Find each integral. $$ \int \cos \frac{\pi t}{2} d t $$

Differentiate each function. $$ f(t)=2 \cos 3 t $$

For each angle: i. Find the radian measure (without using a calculator). ii. Check your answers using a graphing calculator. a. \(30^{\circ}\) b. \(225^{\circ}\) c. \(-180^{\circ}\)

Evaluate without using a calculator. a. \(\tan \frac{3 \pi}{4}\) b. \(\sec \frac{3 \pi}{4}\)

Find each integral. $$ \int \sin \frac{2 t}{5} d t $$

Differentiate each function. $$ f(t)=6 \sin 2 t $$

For each angle: i. Find the radian measure (without using a calculator). ii. Check your answers using a graphing calculator. a. \(15^{\circ}\) b. \(210^{\circ}\) c. \(-90^{\circ}\)

Evaluate without using a calculator. a. \(\tan \frac{7 \pi}{6}\) b. \(\csc \frac{7 \pi}{6}\)

Find each integral. $$ \int \sin (\pi-t) d t $$

Differentiate each function. $$ f(t)=\cos \frac{\pi t}{180} $$

Evaluate without using a calculator, leaving answers in exact form. a. \(\sin \frac{\pi}{3}\) b. \(\cos \frac{\pi}{3}\) c. \(\sin \frac{\pi}{4}\) d. \(\cos \frac{\pi}{4}\)

For each angle: i. Find the radian measure (without using a calculator). ii. Check your answers using a graphing calculator. a. \(60^{\circ}\) b. \(315^{\circ}\) c. \(-120^{\circ}\)

Evaluate without using a calculator. a. \(\tan \frac{5 \pi}{3}\) b. \(\cot \frac{5 \pi}{3}\)

Find each integral. $$ \int \cos (1-t) d t $$

Differentiate each function. $$ f(t)=\sin \frac{\pi t}{200} $$

Evaluate without using a calculator, leaving answers in exact form. a. \(\sin \frac{3 \pi}{4}\) b. \(\cos \frac{3 \pi}{4}\) c. \(\sin \frac{5 \pi}{3}\) d. \(\cos \frac{5 \pi}{3}\)

For each angle: i. Find the radian measure (without using a calculator). ii. Check your answers using a graphing calculator. a. \(45^{\circ}\) b. \(240^{\circ}\) c. \(-150^{\circ}\)

Use a calculator to approximate each value. $$ \cot \frac{\pi}{5} $$

Find each integral. $$ \int \cos \frac{2 \pi(t+20)}{365} d t $$

Differentiate each function. a. \(f(t)=t^{2}+\sin \pi t\) b. Find \(f^{\prime}(0)\)

Evaluate without using a calculator, leaving answers in exact form. a. \(\sin \frac{5 \pi}{4}\) b. \(\cos \frac{5 \pi}{4}\) c. \(\sin \frac{5 \pi}{6}\) d. \(\cos \frac{5 \pi}{6}\)

For each angle: i. Find the radian measure (without using a calculator). ii. Check your answers using a graphing calculator. a. \(540^{\circ}\) b. \(135^{\circ}\) c. \(1^{\circ}\)

Use a calculator to approximate each value. $$ \sec \frac{\pi}{7} $$

Find each integral. $$ \int \sin \frac{\pi(t+3)}{26} d t $$

Evaluate without using a calculator, leaving answers in exact form. a. \(\sin \frac{11 \pi}{6}\) b. \(\cos \frac{11 \pi}{6}\) c. \(\sin \frac{7 \pi}{4}\) d. \(\cos \frac{7 \pi}{4}\)

For each angle: i. Find the radian measure (without using a calculator). ii. Check your answers using a graphing calculator. a. \(750^{\circ}\) b. \(150^{\circ}\) c. \(10^{\circ}\)

Differentiate each function. a. \(f(t)=t \cos \pi t\) b. Find \(f^{\prime}(0)\)

Use a calculator to approximate each value. $$ \sec \frac{5 \pi}{12} $$

Find each integral. $$ \int \sin ^{2} t \cos t d t $$

Differentiate each function. a. \(f(t)=4 \cos \frac{t}{2}\) b. Find \(f^{\prime}\left(\frac{\pi}{3}\right)\)