Angles and the Trigonometric Functions

Trigonometric Functions graphs, Inverse Trigonometric Functions

Trigonometric Identities and Equations

Laws of Sines, Cosines and Vectors

Complex Numbers, Polar Coordinates and Parametric Equations

In Exercises 63–82, use a sketch to find the exact value of each expression.

cot (csc⁻¹ 8)

In Exercises 63–82, use a sketch to find the exact value of each expression.

tan [cos⁻¹ (− 1/3)]

In Exercises 29–51, find the exact value of each expression. Do not use a calculator.

sec⁻¹ (−1)

In Exercises 29–51, find the exact value of each expression. Do not use a calculator.

tan[sin⁻¹ (− 1/2)]

Composition of a trig function with the inverse of another trig function: problem type 2

In Exercises 29–51, find the exact value of each expression. Do not use a calculator.

tan [cos⁻¹ (− 4/5)]

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

Inverse Trigonometric Functions, Part 1 (Basic Introduction)

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

Evaluate Inverse Tangent Expressions Using the Unit Circle

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)

Inverse Cosine Function

Inverse Tangent Function

Find Exact Values of Composite Functions with Inverse Trigonometric Functions

Inverse Trigonometric Functions

Inverse Trigonometric Functions, Part 2 (Evaluating Inverse Trig Functions)

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

In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator.

tan (tan⁻¹ 125)

In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator.

tan⁻¹ (tan 2π/3)

In Exercises 63–82, use a sketch to find the exact value of each expression.

cos [tan⁻¹ (− 2/3)]

Calculator to evaluate inverse trig function

In Exercises 29–51, find the exact value of each expression. Do not use a calculator.

sin⁻¹(sin π/3)

In Exercises 29–51, find the exact value of each expression. Do not use a calculator.

cos⁻¹ (− 1/2)

In Exercises 63–82, use a sketch to find the exact value of each expression.

cos (sin⁻¹ 4/5)

In Exercises 1–26, find the exact value of each expression.

sin⁻¹ 1/2

Evaluate Inverse Sine Expressions Using the Unit Circle

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)

Inverse Trig Functions: Arctan

Inverse Reciprocal Trig on TI 84 Graphing Calculator

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)

Learn How to Find the Angle Given the Inverse Cosine of a Value

In Exercises 29–51, find the exact value of each expression. Do not use a calculator.

sin⁻¹(cos 2π/3)

In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator.

sin⁻¹ (sin 5π/6)

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)

TI Calculator Tutorial: Inverse Trigonometry.

In Exercises 63–82, use a sketch to find the exact value of each expression.

tan [sin⁻¹ (− 3/5)]

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

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)

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

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

sin⁻¹ 0.3

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

How to evaluate for the composition of two trigonometric functions

In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator.

tan⁻¹ [tan(− π/6)]

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

In Exercises 29–51, find the exact value of each expression. Do not use a calculator.

sin(cos⁻¹ 3/5)

PreCalculus - Trigonometry Inverse Cosine Function

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

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

tan⁻¹ (−20)

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

Inverse Trigonometric Functions, Part 3

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.
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sec (sin⁻¹ x/√x²+4)

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

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)

Inverse Sine Function

Inverse Trigonometric Functions, Part 4 (Simplify Expression Using Right Triangle)

Evaluate Inverse Cosine Expressions Using the Reference Triangles

Inverse Trigonometric Functions, Part 5 (Limits)

In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator.

sin(sin⁻¹ 0.9)

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)

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 1–26, find the exact value of each expression.

sin⁻¹ (- 1/2)

Inverse Trigonometric Functions: tan¯¹(x)

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

sin⁻¹ (-0.32)

Inverse Sine Functions

Finding Inverse Trig Functions on a Calculator

Using a calculator to find inverse trig function values

PreCalculus - Trigonometry Inverse Sine Function

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

Evaluate the composition of inverse trig function in terms of x

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

cos⁻¹ 3/8

Integral of 1/(a^2 + x^2) Calculus: u-Substitution

In Exercises 63–82, use a sketch to find the exact value of each expression.

tan (cos⁻¹ 5/13)

In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator.

sin(sin⁻¹ π)

In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator.

sin⁻¹ (sin π)

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

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

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

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

This course covers topics including trigonometric functions (with graphs and inverse functions), identities and equations, solutions of triangles, complex numbers and more.