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Understanding Trigonometric Functions and Their Inverses

This resource explores fundamental trigonometric ratios, such as sine, cosine, tangent, and their respective inverses. It includes various values of tangents, cosecants, and secants, providing a comprehensive overview of how to utilize these functions in mathematical contexts. The document also explains inverse functions, covering their definitions and practical applications, such as solving triangles and equations. Whether you're reviewing inverse sine, cosine, or tangent, this guide serves as an essential tool for mastering trigonometric concepts.

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Understanding Trigonometric Functions and Their Inverses

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  1. 6.4 answers

  2. 1-6

  3. 7-18 7. Tan = 4/3, csc=5/3, sec=5/4 8. Tan= -7/24, csc= -25/7, sec= 25/24, cot= -24/7 9. sin=-15/17, cos= -8/17, tan =15/8, cot= 8/15 10. Sin = ½, cos=-√3/2, tan = -1/√3, cot= -√3 11. sin= 5/13, cos= 13/5, cot=12/5, sec=13/12 12. cos=-4/5, tan= -3/4, csc= 5/3, sec= -5/4 13. cos= 4/5, tan = -3/4, csc=-5/3, sec=5/4 14. cos= -5/13, tan=12/5, csc= -13/12, cot=5/12 15. Sin= -3/5, tan=3/4, csc=-5/3, sec=-5/4, cot=4/3 16. s=24/25, t=24/7, csc= 25/24, sec=25/7, cot=7/24 17. -1 18. -√2

  4. 6.6: Inverse Trig Functions January 13, 2008

  5. Objectives • Review inverse functions • Define and use: • Inverse sine • Inverse cosine • Inverse tan • Solve triangles and equations

  6. Review of Inverse • f-1 will undo f • f(x) = 2x has an inverse of f-1 (x/2)

  7. Inverse sine • y = sin-1 x or y = arcsin • x= sin y for -1 ≤ x ≤ 1 in the interval [-π/2, π/2]

  8. Inverse cosine • y = cos-1 x or y = arccos • x= cos y for -1 ≤ x ≤ 1 in the interval [0, π]

  9. Inverse Tangent • y = tan-1 x or y = arctan • in the interval [-π/2, π/2]

  10. cos-'(I)=.60=115

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