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13.4 Inverse Trigonometric Functions

13.4 Inverse Trigonometric Functions. Algebra 2. Inverse Trigonometric Functions. If -1≤a≤1, then the inverse sine of a is sin -1 a= θ where sin θ =a and -90˚≤ θ≤ 90 ˚ . If -1 ≤ a, then the inverse cosine of a is cos -1 a= θ and -0 ˚≤θ≤ 180 ˚ .

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13.4 Inverse Trigonometric Functions

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  1. 13.4 Inverse Trigonometric Functions Algebra 2

  2. Inverse Trigonometric Functions • If -1≤a≤1, then the inverse sine of a is sin-1a=θ where sinθ=a and -90˚≤θ≤90˚. • If -1≤a, then the inverse cosine of a is cos-1a=θ and -0˚≤θ≤180˚. • If a is any real number, then the inverse tangent of a is tan-1θ=a where tanθ=a and -90˚<θ<90.˚

  3. Examples: • Evaluate the expression in both radians and degrees.

  4. Examples: • Evaluate the expression in both radians and degrees.

  5. Examples: • Evaluate the expression in both radians and degrees.

  6. Other Examples:

  7. Examples: • Find the measure of the angle θ for the triangles shown. 12 7 θ

  8. Examples: • Find the measure of the angle θ for the triangles shown. θ 13 18

  9. Other Examples:

  10. Example: • Solve the equation where 180˚<θ<270˚

  11. Example: • Solve the equation where 90˚<θ<180˚

  12. Other Examples:

  13. Example: • A sand pile in a yard is 4 feet high. A diameter of its base is 10 feet. • Find the angle of repose for this pile of sand. • How tall will a pile of this sand be if the base has a diameter of 40 feet?

  14. Example: • A crane whose lower end is 4 feet off the ground has a 100 foot arm. The arm has to reach the top of a building 80 feet high. At what angle should the arm be set?

  15. Example: • A 10 inch high pile of sand in a sandbox has a diameter of 35 inches. • What is the angle of repose for this sand? • How wide will a pile 18 inches high be?

  16. Other Examples

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