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Unit 12 – Trigonometry Study Sheet Right Triangle Trig: O A O S C T H H A Angle of Elevation: line of sight is titled upward angle of elevation forms a right angle horizontal line Angle of Depression: line of sight is titled downward horizontal line angle of depression forms a right angle horizontal line Remember: The measure of the angle of depression is equal to the measure of the angle of elevation. Reciprocal Trig Functions sin θ opposite hypotenuse cos θ adjacent hypotenuse tan θ opposite adjacent csc θ hypotenuse opposite sec θ hypotenuse adjacent cot θ adjacent opposite To find a coterminal angle Add or subtract 360° from the given angle Converting between radians and degrees: The measure of any angle can be expressed in degrees or in radians. We can do this by forming the following proportion: OR To convert from DEGREES to RADIANS: Multiply by 180 . To convert from RADIANS to DEGREES: 180 Multiply by . Clock Problems – Find the number of radians in the angle formed by hands of a clock. Special Right Triangles: 30 – 60 – 90 30° 45 – 45 – 90 45° 2 1 60° 45° 1 1 Reference Angles: S A T C reference angle reference angle A reference angle is the angle formed by the terminal side of the angle in standard position and the x-axis. θ = reference angle reference angle “ASTC” with Reciprocal Trig Functions Sign Chart (ASTC): Sin and Csc are positive (QII) All functions are positive (QI) Tan and Cot are positive (QIII) Cos and Sec are positive (QIV) Reciprocal Identities csc 1 sin sec 1 cos cot Tangent and Cotangent Identities tan sin cos cot Pythagorean Identity Cofunction Identity Sine and cosine are cofunctions. **Remember the relationship between cofunction and complementary** Cofunctions are equal in value only when their angles add to 90o cos sin 1 tan The Unit Circle: (0, 1) (1, 0) (-1, 0) (0, -1)