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Comprehensive Guide to Trigonometric Functions and Identities

This resource provides a detailed overview of trigonometric functions including arcsine, arccosine, and arctangent, along with their graphs, domains, and ranges. It covers the definitions of secant, cosecant, and cotangent, as well as their relationships to the primary functions. Students will learn about radian measure and its equivalence to degrees, along with exact values of sine, cosine, and tangent for key angles. The guide emphasizes the use of unit circle and Pythagoras' theorem to derive relationships and identities, including addition and double angle formulas.

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Comprehensive Guide to Trigonometric Functions and Identities

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  1. Core 3 Trigonometry http://www.tes.co.uk/ResourceDetail.aspx?storyCode=3009773

  2. Know the definitions of arcsin arccos arctan in relation to the three basic trigonometrical functions and the graphs, domainsand ranges of all these functions

  3. Know the definitions of secant cosecant cotangent in relation to the three basic trigonometrical functions and the graphs, domainsand ranges of all these functions

  4. Understand radian measure as an alternative to degree measure, and be able to switch between the two systems

  5. Know the exact values of sin θ, cos θ and tan θ (where defined) for values of θ in the set Θ = {0°,30 °,45 °,60 °,90 °,180 °,270 °,360 °} and their radian equivalents

  6. Know how to use the unit circle and Pythagoras’ Theorem to deduce the relationship between sin θand cos θ and to deduce the equivalent relationships involving sec θ, cosec θ, tan θ and cot θ

  7. Understand and use the Addition (Compound Angle) formulae for sin(A ± B) , cos(A ± B) and tan(A ± B) to deduce the Double Angle Formulae

  8. Understand and use the Addition formulae for sin(A ± B) , cos(A ± B) and tan(A ± B) And other basic trigonometric identities to prove new identities

  9. Know how to derive the Trigonometric Factor Formulae from the Trigonometric Addition Formulae Know how to use the Factor Formulae to write a sum or difference using sin θ or cos θ to a product using sin θ and cos θ

  10. Know how to use the standard trigonometric identities to find exact values of Trigonometric expressions without a calculator

  11. http://www.gogeometry.com/mindmap/khan_trigonometry_videos_mind_map_elearning.htmlhttp://www.gogeometry.com/mindmap/khan_trigonometry_videos_mind_map_elearning.html

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