Chapter 13

Algebra 2 · 418 exercises

Problem 1

Evaluate each expression. Give your answer as a decimal rounded to the nearest hundredth. $$ \csc 100^{\circ} $$

3 step solution

Problem 1

Use the graph of \(y=\tan \theta\) to find each value. If the tangent is undefined at that point, write undefined. $$ \tan (-\pi) $$

2 step solution

Problem 1

Write each measure in radians. Express the answer in terms of \(\pi\) and as a decimal rounded to the nearest hundredth. $$ -300^{\circ} $$

4 step solution

Problem 2

Evaluate each expression. Give your answer as a decimal rounded to the nearest hundredth. $$ \csc 80^{\circ} $$

4 step solution

Problem 2

What is the value of \(h\) in each translation? Describe each phase shift (use a phrase like 3 units to the left). $$ g(t)=f(t+2) $$

3 step solution

Problem 2

Use the graph of \(y=\tan \theta\) to find each value. If the tangent is undefined at that point, write undefined. $$ \tan \pi $$

2 step solution

Problem 2

Write each measure in radians. Express the answer in terms of \(\pi\) and as a decimal rounded to the nearest hundredth. $$ 150^{\circ} $$

4 step solution

Problem 3

Evaluate each expression. Give your answer as a decimal rounded to the nearest hundredth. $$ \cot \left(-55^{\circ}\right) $$

4 step solution

Problem 3

Use the graph of \(y=\tan \theta\) to find each value. If the tangent is undefined at that point, write undefined. $$ \tan \frac{3 \pi}{4} $$

3 step solution

Problem 3

Write each measure in radians. Express the answer in terms of \(\pi\) and as a decimal rounded to the nearest hundredth. $$ -90^{\circ} $$

4 step solution

Problem 4

Evaluate each expression. Give your answer as a decimal rounded to the nearest hundredth. $$ \sec 200^{\circ} $$

5 step solution

Problem 4

What is the value of \(h\) in each translation? Describe each phase shift (use a phrase like 3 units to the left). $$ h(x)=f(x-3) $$

2 step solution

Problem 4

Use the graph of \(y=\tan \theta\) to find each value. If the tangent is undefined at that point, write undefined. $$ \tan \frac{\pi}{2} $$

2 step solution

Problem 4

Write each measure in radians. Express the answer in terms of \(\pi\) and as a decimal rounded to the nearest hundredth. $$ -60^{\circ} $$

3 step solution

Problem 5

Evaluate each expression. Write your answer in exact form. Suppose \(\tan \theta=\frac{20}{15} .\) Find \(\cot \theta\)

3 step solution

Problem 5

Use the graph of \(y=\tan \theta\) to find each value. If the tangent is undefined at that point, write undefined. $$ \tan \left(-\frac{7 \pi}{4}\right) $$

2 step solution

Problem 5

Sketch the graph of each function in the interval from 0 to 2\(\pi\) \(y=\cos 2 \theta\)

3 step solution

Problem 5

Write each measure in radians. Express the answer in terms of \(\pi\) and as a decimal rounded to the nearest hundredth. $$ 160^{\circ} $$

4 step solution

Problem 5

What is the value of \(h\) in each translation? Describe each phase shift (use a phrase like 3 units to the left). $$ y=\sin (x+\pi) $$

2 step solution

Problem 6

Evaluate each expression. Write your answer in exact form. Suppose \(\sin \theta=\frac{13}{18} \cdot\) Find \(\csc \theta\)

3 step solution

Problem 6

What is the value of \(h\) in each translation? Describe each phase shift (use a phrase like 3 units to the left). $$ y=\cos \left(x-\frac{5 \pi}{7}\right) $$

4 step solution

Problem 6

Use the graph of \(y=\tan \theta\) to find each value. If the tangent is undefined at that point, write undefined. $$ \tan 2 \pi $$

2 step solution

Problem 6

Sketch the graph of each function in the interval from 0 to 2\(\pi\). \(y=-3 \cos \theta\)

3 step solution

Problem 6

Write each measure in radians. Express the answer in terms of \(\pi\) and as a decimal rounded to the nearest hundredth. $$ 20^{\circ} $$

4 step solution

Problem 7

Evaluate each expression. Write your answer in exact form. Suppose cos \(\theta=-\frac{21}{35}\) . Find \(\sec \theta\)

4 step solution

Problem 7

Use the graph of \(y=\tan \theta\) to find each value. If the tangent is undefined at that point, write undefined. $$ \tan \left(-\frac{3 \pi}{4}\right) $$

3 step solution

Problem 7

Sketch the graph of each function in the interval from 0 to 2\(\pi\). \(y=-\cos 3 t\)

4 step solution

Problem 7

Sketch each angle in standard position. $$ 40^{\circ} $$

5 step solution

Problem 7

Write each measure in degrees. Round your answer to the nearest degree, if necessary. 3\(\pi\) radians

3 step solution

Problem 8

Evaluate each expression. Write your answer in exact form. Suppose tan \(\theta=-\frac{4}{3},\) Find \(\cot \theta\)

3 step solution

Problem 8

Use the graph of \(y=\tan \theta\) to find each value. If the tangent is undefined at that point, write undefined. $$ \tan \frac{3 \pi}{2} $$

3 step solution

Problem 8

Sketch the graph of each function in the interval from 0 to 2\(\pi\). \(y=\cos \frac{\pi}{2} \theta\)

3 step solution

Problem 8

Sketch each angle in standard position. $$ -130^{\circ} $$

3 step solution

Problem 8

Write each measure in degrees. Round your answer to the nearest degree, if necessary. \(\frac{11 \pi}{10}\) radians

3 step solution

Problem 9

Find the exact value of each expression. If the expression is undefined, write undefined. $$ \sec 45^{\circ} $$

3 step solution

Problem 9

Sketch the graph of each function in the interval from 0 to 2\(\pi\). \(y=-\cos \pi \theta\)

3 step solution

Problem 9

Sketch each angle in standard position. $$ -270^{\circ} $$

3 step solution

Problem 9

Write each measure in degrees. Round your answer to the nearest degree, if necessary. \(-\frac{2 \pi}{3}\) radians

4 step solution

Problem 10

Find the exact value of each expression. If the expression is undefined, write undefined. $$ \cot 60^{\circ} $$

3 step solution

Problem 10

Write a cosine function for each description. Assume that \(a>0\). amplitude \(2,\) period \(\pi\)

3 step solution

Problem 10

Sketch each angle in standard position. $$ 120^{\circ} $$

3 step solution

Problem 10

Write each measure in degrees. Round your answer to the nearest degree, if necessary. \(-3\) radians

4 step solution

Problem 11

Find the exact value of each expression. If the expression is undefined, write undefined. $$ \cot 90^{\circ} $$

3 step solution

Problem 11

Graph each translation of \(y=\cos x\) in the interval from 0 to 2\(\pi\) $$ y=\cos (x+3) $$

3 step solution

Problem 11

Identify the period and tell where two asymptotes occur for each function. $$ y=\tan 5 \theta $$

2 step solution

Problem 11

Write a cosine function for each description. Assume that \(a>0\). amplitude \(\frac{\pi}{2},\) period 3

4 step solution

Problem 11

Sketch each angle in standard position. $$ 95^{\circ} $$

4 step solution

Problem 11

Write each measure in degrees. Round your answer to the nearest degree, if necessary. 1.57 radians

3 step solution

Problem 12

Find the exact value of each expression. If the expression is undefined, write undefined. $$ \sec 180^{\circ} $$

3 step solution

Problem 12

Graph each translation of \(y=\cos x\) in the interval from 0 to 2\(\pi\) $$ y=\cos x+3 $$

3 step solution

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