Section/Topic5.1 Fundamental Identities CC High School Functions Trigonometric Functions: Prove and apply trigonometric identities Objective Students will be able to prove trigonometric identities Homework P191 (5-10, 15-22) Trig Game PlanDate: 11/15/13

Fundamental Identities Reciprocal Identities Quotient Identities

Fundamental Identities Pythagorean Identities Negative-Angle Identities

Note In trigonometric identities, θ can be an angle in degrees, an angle in radians, a real number, or a variable.

If and θ is in quadrant II, find each function value. FINDING TRIGONOMETRIC FUNCTION VALUES GIVEN ONE VALUE AND THE QUADRANT (a)sec θ In quadrant II, sec θ is negative, so Pythagorean identity Example 1: We Do

(b)sin θ from part (a) Quotient identity Reciprocal identity FINDING TRIGONOMETRIC FUNCTION VALUES GIVEN ONE VALUE AND THE QUADRANT Example 1: We Do

(c)cot(– θ) Reciprocal identity Negative-angle identity FINDING TRIGONOMETRIC FUNCTION VALUES GIVEN ONE VALUE AND THE QUADRANT Example 1: We Do _

If and is in quadrant IV, find each function value. (a) In quadrant IV, is negative. FINDING TRIGONOMETRIC FUNCTION VALUES GIVEN ONE VALUE AND THE QUADRANT Example 2: You Do 2gether

If and is in quadrant IV, find each function value. (b) (c) FINDING TRIGONOMETRIC FUNCTION VALUES GIVEN ONE VALUE AND THE QUADRANT Example 2: You Do 2gether

FINDING TRIGONOMETRIC FUNCTION VALUES GIVEN ONE VALUE AND THE QUADRANT Example 3: You Do 2gether

Caution To avoid a common error, when taking the square root, be sure to choose the sign based on the quadrant of θ and the function being evaluated.

Speed Test Reciprocal Identities (6) Quotient identities (2) Pythagorean identities (3) Cofunction identities (6)