{"id":10282,"date":"2026-07-03T17:39:42","date_gmt":"2026-07-03T17:39:42","guid":{"rendered":"https:\/\/kapdec.com\/help\/?p=10282"},"modified":"2026-07-03T17:39:42","modified_gmt":"2026-07-03T17:39:42","slug":"properties-and-principles-of-trigonometry","status":"publish","type":"post","link":"https:\/\/kapdec.com\/help\/properties-and-principles-of-trigonometry\/","title":{"rendered":"Properties And Principles Of Trigonometry"},"content":{"rendered":"
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KAPDEC® | Elite STEM Learning Platform | https:\/\/kapdec.com<\/a><\/p>\n

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Unit\u00a0 – TRIANGLES & TRIGONOMETRY<\/strong><\/h2>\n

Chapter: – Properties & Principal of Trigonometry<\/strong><\/h3>\n

What students will learn in this Section<\/strong><\/p>\n

In the Trigonometry & Triangles section of the SAT, students delve into the intricacies of triangle geometry. They discern the distinguishing features of Equilateral, Isosceles, and Scalene triangles, grasping not only their side-length characteristics but also the corresponding angle properties. The introduction of trigonometric functions\u2014Sine, Cosine, and Tangent\u2014equips students with tools to navigate the relationships between sides and angles in right-angled triangles.<\/p>\n

Beyond triangles, students explore the sum of interior angles in triangles and the properties of angles within quadrilaterals. This comprehensive understanding enables them to approach a myriad of geometry problems presented in the SAT, fostering critical thinking and analytical skills essential for success in the Math section.<\/p>\n

Important Definitions<\/u><\/strong>:<\/p>\n

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  • Equilateral Triangle:<\/strong>\n
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    • A triangle with all three sides of equal length.<\/li>\n<\/ul>\n<\/li>\n
    • Isosceles Triangle:<\/strong>\n
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      • A triangle with at least two sides of equal length.<\/li>\n<\/ul>\n<\/li>\n
      • Scalene Triangle:<\/strong>\n
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        • A triangle with all three sides of different lengths.<\/li>\n<\/ul>\n<\/li>\n
        • Sine (sin):<\/strong>\n
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          • In a right-angled triangle, the ratio of the length of the side opposite an angle to the length of the hypotenuse.<\/li>\n<\/ul>\n<\/li>\n
          • Cosine (cos):<\/strong>\n
              \n
            • In a right-angled triangle, the ratio of the length of the side adjacent to an angle to the length of the hypotenuse.<\/li>\n<\/ul>\n<\/li>\n
            • Tangent (tan):<\/strong>\n
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              • In a right-angled triangle, the ratio of the length of the side opposite an angle to the length of the side adjacent to the angle.<\/li>\n<\/ul>\n<\/li>\n
              • Parallelogram:<\/strong><\/li>\n
              • A quadrilateral with opposite sides equal and parallel.<\/li>\n
              • Rectangle:<\/strong><\/li>\n
              • A parallelogram with all angles equal to 90 degrees.<\/li>\n
              • Rhombus:<\/strong><\/li>\n
              • A parallelogram with all sides equal.<\/li>\n<\/ul>\n

                Important Formulae<\/u><\/strong>:<\/p>\n

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                1. Lines and Angles:<\/strong>\n
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                  • Slope of a Line (m):<\/em> m<\/em>=\n
                    \"\"<\/p>\n

                    Source: Kapdec.com<\/p>\n<\/div>\n<\/li>\n

                  • Distance Formula between two points (P1<\/sub>(x1<\/sub>, y1<\/sub>) and P2<\/sub>(x2<\/sub>, y2<\/sub>)):<\/em><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n

                    \"\"<\/p>\n

                    Source: Kapdec.com<\/p>\n<\/div>\n

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                    1. Complementary and Supplementary Angles:<\/strong>\n
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                      • Complementary Angles:<\/em> \u2220A<\/em>+\u2220B<\/em>=90\u2218<\/li>\n
                      • Supplementary Angles:<\/em> \u00a0\u2220C<\/em>+\u2220D<\/em>=180\u2218<\/li>\n<\/ul>\n<\/li>\n
                      • Triangles:<\/strong>\n
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                        • Sum of Interior Angles of a Triangle:<\/em> Sum=180\u2218<\/li>\n
                        • Pythagorean Theorem (for a right-angled triangle ABC with hypotenuse c):<\/em> a<\/em>2<\/sup>+b<\/em>2<\/sup>=c<\/em>2<\/sup><\/li>\n<\/ul>\n<\/li>\n
                        • Special Right Triangles:<\/strong>\n
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                          • 45-45-90 Triangle:<\/em> If the acute angles are both 45 degrees, then the sides are in the ratio 1:1:\u221a2.<\/li>\n
                          • 30-60-90 Triangle:<\/em> If the angles are 30, 60, and 90 degrees, then the sides are in the ratio 1:\u221a3:2.<\/li>\n<\/ul>\n<\/li>\n
                          • Area Formulas:<\/strong>\n
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                            • Area of a Triangle (given base b and height h):<\/em> Area=\n
                              \"\"<\/p>\n

                              Source: Kapdec.com<\/p>\n<\/div>\n

                              \u200b\u00d7b<\/em>\u00d7h<\/em><\/li>\n

                            • Area of a Right-Angled Triangle (given legs a and b):<\/em> Area=\u200b\n
                              \"\"<\/p>\n

                              Source: Kapdec.com<\/p>\n<\/div>\n

                              \u00d7a<\/em>\u00d7b<\/em><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n

                              Speed Strategy<\/u><\/strong><\/p>\n

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                              1. Memorize Key Formulas:<\/strong>\n
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                                • Memorize essential formulas to reduce the time spent looking them up. This includes formulas for Area, sector Angles, Tangent line equation, and other geometrical measures.<\/li>\n<\/ul>\n<\/li>\n
                                • Practice Formula Rearrangement:<\/strong>\n
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                                  • Familiarize yourself with rearranging formulas. This skill allows you to quickly solve for different variables without having to derive the entire formula.<\/li>\n<\/ul>\n<\/li>\n
                                  • Use Pre-calculated Constants:<\/strong>\n
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                                    • Pre-calculate constants or values that frequently appear in formulas. For example, memorize common Z-scores or values associated with circles & Angles.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n

                                      \u00a0<\/p>\n

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