Transcription of 5-1 Study Guide and Intervention - MRS. FRUGE
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5-1 Study Guide and Intervention - MRS. FRUGE
NAME _____ DATE _____ PERIOD _____ Chapter 5 5 Glencoe Precalculus 5-1 Study Guide and Intervention Trigonometric Identities Basic Trigonometric Identities An equation is an identity if the left side is equal to the right side for all values of the variable for which both sides are defined. Trigonometric identities are identities that involve trigonometric functions. Reciprocal Identities Pythagorean Identities sin = 1csc csc = 1sin cos = 1sec sec = 1cos tan = 1cot cot = 1tan sin2 + cos2 = 1 tan2 + 1 = sec2 cot2 + 1 = csc2 Example: If sin = and 0 < < 90 , find tan . Use two identities to relate sin and tan . sin2 + cos2 = 1 Pythagorean Identity (35)2 + cos2 = 1 sin = 35 cos2 = 1625 Simplify. cos = 1625 or 45 Take the square root of each side. Since 0 < < 90 , cos is positive. Thus, cos = 45. Now find tan . tan = sin cos Quotient identity tan = 3545 sin = 35, cos = 45 tan = 34 Simplify.
5-1 Study Guide and Intervention Trigonometric Identities Basic Trigonometric Identities An equation is an identity if the left side is equal to the right side for all values of the variable for which both sides are defined. Trigonometric identities are identities that involve trigonometric functions.
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