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(Study of relationships between the sides and angles of a triangle.) 1. Trigonometric Ratios: Ratios of the sides of a right triangle with respect to its acute angles ~ In right triangle ABC, is an acute angle 2. 3. 4. If one of the trigonometric ratios of an acute angle is known, the remaining trigonometric ratios of the angle can be easily determined. 5. Trigonometric Ratios Of Some Specific Angles: 6. The value of sin A and cos A never exceeds 1, whereas the value of sec A or cosec A is always greater than or equal to 1. 7. Trigonometric Ratios Of Complementary Angles: Two angles are said to be complementary if their sum equals 90 . 𝒔𝒊𝒏 𝟗𝟎 – 𝑨 𝒔𝒊𝒏𝑩 𝒄𝒐𝒔 𝑨, 𝒄𝒐𝒔 𝟗𝟎 – 𝑨 𝒄𝒐𝒔𝑩 𝒔𝒊𝒏 𝑨, 𝒕𝒂𝒏 𝟗𝟎 – 𝑨 𝒕𝒂𝒏𝑩 𝒄𝒐𝒕 𝑨, 𝒄𝒐𝒕 𝟗𝟎 – 𝑨 𝒄𝒐𝒕𝑩 𝒕𝒂𝒏 𝑨, 𝒔𝒆𝒄 𝟗𝟎 – 𝑨 𝒔𝒆𝒄𝑩 𝒄𝒐𝒔𝒆𝒄 𝑨, 𝒄𝒐𝒔𝒆𝒄 𝟗𝟎 – 𝑨 𝒄𝒐𝒔𝒆𝒄𝑩 𝒔𝒆𝒄 𝑨. 8. Three Fundamental Trigonometric Identities: An equation involving trigonometric ratios of an angle is called a trigonometric identity, if it is true for all values of the angle(s) involved. 𝒔𝒊𝒏𝟐 A + 𝒄𝒐𝒔𝟐 A = 1, 𝒔𝒆𝒄𝟐 A – 𝒕𝒂𝒏𝟐 A = 1 𝒄𝒐𝒔𝒆𝒄𝟐 A = 1 + 𝒄𝒐𝒕𝟐 A