Channels

The following equations cannot be solved by algebraic methods. Use a graphing calculator to find all solutions over the interval [0, 6]. Express solutions to four decimal places.

(arctan x)³ ― x + 2 = 0

140

views

Textbook Question

Use a calculator to approximate each value in decimal degrees.

θ = arccos (-0.39876459)

152

views

Textbook Question

Use a calculator to approximate each value in decimal degrees.

θ = csc⁻¹ 1.9422833

144

views

Textbook Question

Use a calculator to approximate each value in decimal degrees.

θ = cot⁻¹ (-0.60724226)

160

views

Textbook Question

Solve each equation for x.

4/3 arctan x/2 = π

145

views

Textbook Question

Solve each equation for x.

arccos x + arctan 1 = 11π/12

146

views

Textbook Question

Use a calculator to approximate each value in decimal degrees.

θ = tan⁻¹ (-7.7828641)

131

views

Textbook Question

Use a calculator to approximate each real number value. (Be sure the calculator is in radian mode.)

y = arcsin 0.92837781

152

views

Textbook Question

Use a calculator to approximate each real number value. (Be sure the calculator is in radian mode.)

y = cos⁻¹ (―0.32647891)

149

views

Textbook Question

Solve each equation for x.

y = 1/2 tan (3x + 2), for x in [-2/3 - π/6, -2/3 + π/6]

147

views

Textbook Question

Use a calculator to approximate each real number value. (Be sure the calculator is in radian mode.)

y = arctan 1.1111111

160

views

Textbook Question

Use a calculator to approximate each real number value. (Be sure the calculator is in radian mode.)

y = cot⁻¹ (―0.92170128)

136

views

Textbook Question

Use a calculator to approximate each real number value. (Be sure the calculator is in radian mode.)

y = sec⁻¹ (―1.2871684)

149

views

Textbook Question

Solve each equation for x, where x is restricted to the given interval.

y = 5 cos x , for x in [0, π]

135

views

Textbook Question

Find the exact value of each real number y. Do not use a calculator.

y = tan⁻¹ (―√3)

152

views

Textbook Question

Graph each inverse circular function by hand.

y = arcsec [(1/2)x]

146

views

Textbook Question

Evaluate each expression without using a calculator.

tan (arccos 3/4)

157

views

Textbook Question

Evaluate each expression without using a calculator.

cos (tan⁻¹ (-2))

155

views

Textbook Question

Evaluate each expression without using a calculator.

sin (2 tan⁻¹ (12/5))

134

views

Textbook Question

Evaluate each expression without using a calculator.

cos (2 arctan (4/3))

142

views

Textbook Question

Evaluate each expression without using a calculator.

sin (2 cos⁻¹ (1/5))

161

views

Textbook Question

Evaluate each expression without using a calculator.

sec (sec⁻¹ 2)

161

views

Textbook Question

Evaluate each expression without using a calculator.

cos (tan⁻¹ (5/12) - tan⁻¹ (3/4))

194

views

Textbook Question

Evaluate each expression without using a calculator.

sin (sin⁻¹ 1/2 + tan⁻¹ (-3))

153

views

Textbook Question

Solve each equation for x, where x is restricted to the given interval.

y = 3 tan 2x , for x in [―π/4, π/4]

135

views

Textbook Question

Find the exact value of each real number y. Do not use a calculator.

y = cos⁻¹ (―√2/2)

167

views

Textbook Question

Use a calculator to find each value. Give answers as real numbers.

cos (tan⁻¹ 0.5)

146

views

Textbook Question

Use a calculator to find each value. Give answers as real numbers.

tan (arcsin 0.12251014)

148

views

Textbook Question

Write each trigonometric expression as an algebraic expression in u, for u > 0.

sin (arccos u)

187

views

Textbook Question

Write each trigonometric expression as an algebraic expression in u, for u > 0.

cos (arcsin u)

142

views

Textbook Question

Write each trigonometric expression as an algebraic expression in u, for u > 0.

sin (2 sec⁻¹ u/2)

197

views

Textbook Question

In Exercises 1–26, find the exact value of each expression. _ cos⁻¹ √3/2

205

views

Textbook Question

In Exercises 1–26, find the exact value of each expression. _ cos⁻¹ (- √2/2)

217

views

Textbook Question

In Exercises 1–26, find the exact value of each expression. _ tan⁻¹ √3/3

213

views

Textbook Question

In Exercises 1–26, find the exact value of each expression. _ tan⁻¹ (−√3)

224

views

Textbook Question

In Exercises 1–26, find the exact value of each expression. _ cot⁻¹ √3

218

views

Textbook Question

In Exercises 1–26, find the exact value of each expression. _ cot⁻¹ (−√3)

222

views

Textbook Question

In Exercises 1–26, find the exact value of each expression. _ csc⁻¹ (− 2√3/3)

292

views

Textbook Question

In Exercises 1–26, find the exact value of each expression. _ sec⁻¹ (−√2)

217

views

Textbook Question

In Exercises 27–38, use a calculator to find the value of each expression rounded to two decimal places. sin⁻¹ 0.3

207

views

Textbook Question

In Exercises 27–38, use a calculator to find the value of each expression rounded to two decimal places. sin⁻¹ (-0.32)

217

views

Textbook Question

In Exercises 27–38, use a calculator to find the value of each expression rounded to two decimal places. cos⁻¹ 3/8

215

views

Textbook Question

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. _ sin⁻¹ (− √3/2)

214

views

Textbook Question

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. cos⁻¹ (− 1/2)

224

views

Textbook Question

In Exercises 27–38, use a calculator to find the value of each expression rounded to two decimal places. _ cos⁻¹ √5/7

282

views

Textbook Question

In Exercises 27–38, use a calculator to find the value of each expression rounded to two decimal places. tan⁻¹ (−20)

237

views

Textbook Question

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. sec⁻¹ (−1)

208

views

Textbook Question

In Exercises 27–38, use a calculator to find the value of each expression rounded to two decimal places. ___ tan⁻¹ (−√473)

216

views

Textbook Question

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. _ cos(sin⁻¹ √2/2)

228

views

Textbook Question

In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator. sin(sin⁻¹ 0.9)

186

views

Textbook Question

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. tan[sin⁻¹ (− 1/2)]

225

views

Textbook Question

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. _ csc(tan⁻¹ √3/3)

225

views

Textbook Question

In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator. sin⁻¹ (sin 5π/6)

233

views

Textbook Question

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. sin(cos⁻¹ 3/5)

220

views

Textbook Question

In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator. tan (tan⁻¹ 125)

218

views

Textbook Question

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. tan [cos⁻¹ (− 4/5)]

245

views

Textbook Question

In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator. tan⁻¹ [tan(− π/6)]

231

views

Textbook Question

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. sin⁻¹(sin π/3)

235

views

Textbook Question

In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator. tan⁻¹ (tan 2π/3)

212

views

Textbook Question

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. sin⁻¹(cos 2π/3)

219

views

Textbook Question

In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator. sin⁻¹ (sin π)

239

views

Textbook Question

In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator. sin(sin⁻¹ π)

239

views

Textbook Question

In Exercises 52–53, use a right triangle to write each expression as an algebraic expression. Assume that x is positive and that the given inverse trigonometric function is defined for the expression in x. sec(sin⁻¹ 1/x)

182

views

Textbook Question

In Exercises 55–62, use the properties of inverse functions f(f⁻¹ (x)) = x for all x in the domain of f⁻¹ and f⁻¹(f(x)) for all x in the domain of f, as well as the definitions of the inverse cotangent, cosecant, and secant functions, to find the exact value of each expression, if possible. cot(cot⁻¹ 9π)

225

views

Textbook Question

In Exercises 55–62, use the properties of inverse functions f(f⁻¹ (x)) = x for all x in the domain of f⁻¹ and f⁻¹(f(x)) for all x in the domain of f, as well as the definitions of the inverse cotangent, cosecant, and secant functions, to find the exact value of each expression, if possible. sec(sec⁻¹ 7π)

207

views

Textbook Question

In Exercises 55–62, use the properties of inverse functions f(f⁻¹ (x)) = x for all x in the domain of f⁻¹ and f⁻¹(f(x)) for all x in the domain of f, as well as the definitions of the inverse cotangent, cosecant, and secant functions, to find the exact value of each expression, if possible. cot⁻¹ (cot 3π/4)

238

views

Textbook Question

In Exercises 63–82, use a sketch to find the exact value of each expression. cos (sin⁻¹ 4/5)

200

views

Textbook Question

In Exercises 63–82, use a sketch to find the exact value of each expression. tan (cos⁻¹ 5/13)

208

views

Textbook Question

In Exercises 63–82, use a sketch to find the exact value of each expression. tan [sin⁻¹ (− 3/5)]

237

views

Textbook Question

In Exercises 63–82, use a sketch to find the exact value of each expression. _ sin (cos⁻¹ √2/2)

362

views

Textbook Question

In Exercises 63–82, use a sketch to find the exact value of each expression. tan [cos⁻¹ (− 1/3)]

276

views

Textbook Question

In Exercises 63–82, use a sketch to find the exact value of each expression. cos [tan⁻¹ (− 2/3)]

198

views

Textbook Question

In Exercises 63–82, use a sketch to find the exact value of each expression. cot (csc⁻¹ 8)

215

views

Textbook Question

In Exercises 83–94, use a right triangle to write each expression as an algebraic expression. Assume that x is positive and that the given inverse trigonometric function is defined for the expression in x. tan (cos⁻¹ x)

In Exercises 83–94, use a right triangle to write each expression as an algebraic expression. Assume that x is positive and that the given inverse trigonometric function is defined for the expression in x. sin (tan⁻¹ x)

355

views

Textbook Question

In Exercises 83–94, use a right triangle to write each expression as an algebraic expression. Assume that x is positive and that the given inverse trigonometric function is defined for the expression in x. cos (sin⁻¹ 1/x)

228

views

Textbook Question

In Exercises 83–94, use a right triangle to write each expression as an algebraic expression. Assume that x is positive and that the given inverse trigonometric function is defined for the expression in x. sec (cos⁻¹ 1/x)

208

views

Textbook Question

In Exercises 83–94, use a right triangle to write each expression as an algebraic expression. Assume that x is positive and that the given inverse trigonometric function is defined for the expression in x. ___ sec (sin⁻¹ x/√x²+4)

214

views

Textbook Question

In Exercises 83–94, use a right triangle to write each expression as an algebraic expression. Assume that x is positive and that the given inverse trigonometric function is defined for the expression in x. csc (cot⁻¹ x)

268

views

Textbook Question

The graphs of y = sin⁻¹ x, y = cos⁻¹ x, and y = tan⁻¹ x are shown in Table 2.8. In Exercises 97–106, use transformations (vertical shifts, horizontal shifts, reflections, stretching, or shrinking) of these graphs to graph each function. Then use interval notation to give the function's domain and range. f(x) = sin⁻¹ x + π/2

173

views

Textbook Question

The graphs of y = sin⁻¹ x, y = cos⁻¹ x, and y = tan⁻¹ x are shown in Table 2.8. In Exercises 97–106, use transformations (vertical shifts, horizontal shifts, reflections, stretching, or shrinking) of these graphs to graph each function. Then use interval notation to give the function's domain and range. f(x) = cos⁻¹ (x + 1)

183

views

Textbook Question

The graphs of y = sin⁻¹ x, y = cos⁻¹ x, and y = tan⁻¹ x are shown in Table 2.8. In Exercises 97–106, use transformations (vertical shifts, horizontal shifts, reflections, stretching, or shrinking) of these graphs to graph each function. Then use interval notation to give the function's domain and range. h(x) = −2 tan⁻¹ x

179

views

Textbook Question

The graphs of y = sin⁻¹ x, y = cos⁻¹ x, and y = tan⁻¹ x are shown in Table 2.8. In Exercises 97–106, use transformations (vertical shifts, horizontal shifts, reflections, stretching, or shrinking) of these graphs to graph each function. Then use interval notation to give the function's domain and range. f(x) = cos⁻¹ x/2

163

views

My Courses

Chemistry

Biology

Math

Physics

Business

Social Sciences

Programming

Product & Marketing

5. Inverse Trigonometric Functions and Basic Trigonometric Equations

Inverse Sine, Cosine, & Tangent

Learn with Callie

Learn with other creators

Practice this topic