0. Functions

An inverse tangent identity

b. Prove that tan⁻¹ x + tan⁻¹ x(1/x) = π/2, for x > 0.

Verify the identity sec⁻¹ x = cos⁻¹ (1/x), for x ≠ 0.

Evaluating hyperbolic functions Use a calculator to evaluate each expression or state that the value does not exist. Report answers accurate to four decimal places to the right of the decimal point.

c. csch⁻¹ 5

Evaluating hyperbolic functions Use a calculator to evaluate each expression or state that the value does not exist. Report answers accurate to four decimal places to the right of the decimal point.

f. tan⁻¹(sinh x) |₋₃³

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.

1. a. arctan 1

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.

1. c. tan^(-1)(1/√3)

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.

2. b. tan^(-1)(√3)

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.

3. a. arcsin(-1/2)

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.

3. c. sin^(-1)(-√3/2)

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.

4. b. arcsin(-1/√2)

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.

5. a. arccos(1/2)

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.

5. c. arccos(√3/2)

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.

6. b. arccsc(-2/√3)

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.

7. a. sec^(-1)(-√2)

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.

7. c. arcsec(-2)