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Warm-Up

Warm-Up. If (2, -5) is on the terminal side of an angle α in standard position, find the 6 trig functions. If cos α <0 and cot >0, in what quadrant does α terminate? If cos α = 4/5 and α is in quadrant IV, find the values of cosecant and secant. . Trig Game Plan Date: 9/23/13.

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Warm-Up

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  1. Warm-Up • If (2, -5) is on the terminal side of an angle α in standard position, find the 6 trig functions. • If cos α <0 and cot >0, in what quadrant does α terminate? • If cos α = 4/5 and α is in quadrant IV, find the values of cosecant and secant.

  2. Trig Game Plan Date: 9/23/13

  3. Right-Triangle-Based Definitions of Trigonometric Functions For any acute angle A in standard position,

  4. Right-Triangle-Based Definitions of Trigonometric Functions (page 62) For any acute angle A in standard position,

  5. FINDING TRIGONOMETRIC FUNCTION VALUES OF AN ACUTE ANGLE Example 1 Find the sine, cosine, and tangent values for angles A and B.

  6. FINDING TRIGONOMETRIC FUNCTION VALUES OF AN ACUTE ANGLE (cont.) Example 1 Find the sine, cosine, and tangent values for angles A and B.

  7. CofunctionIdentities (page 63) For any acute angle A in standard position, sin A = cos(90  A) cscA = sec(90  A) tan A = cot(90  A) cosA = sin(90  A) sec A = csc(90  A) cot A = tan(90  A)

  8. WRITING FUNCTIONS IN TERMS OF COFUNCTIONS Example 2a Write each function in terms of its cofunction. (a) cos 52° = sin (90° – 52°) = sin 38° (b) tan 71° = cot (90° – 71°) = cot 19° (c) sec 24° = csc (90° – 24°) = csc 66°

  9. WRITING FUNCTIONS IN TERMS OF COFUNCTIONS Example 2b • Write each function in terms of its cofunction. (a) sin 9° = cos (90° – 9°) = cos 81° (b) cot 76° = tan (90° – 76°) = tan 14° (c) csc 45° = sec (90° – 45°) = sec 45°

  10. SOLVING EQUATIONS USING THE COFUNCTION IDENTITIES Example 3a Find one solution for the equation. Assume all angles involved are acute angles. (a) Fsin(θ+4)=cos(3θ+2) Since sine and cosine are cofunctions, the equation is true if the sum of the angles is 90º. Combine terms. Subtract 6°. Divide by 4.

  11. SOLVING EQUATIONS USING THE COFUNCTION IDENTITIES (continued) Example 3a Find one solution for the equation. Assume all angles involved are acute angles. (b) Ftan(2θ-18)=cot(θ+18) Since tangent and cotangent are cofunctions, the equation is true if the sum of the angles is 90º.

  12. Example 3b • Find one solution for the equation. Assume all angles involved are acute angles. (a) Since cotangent and tangent are cofunctions, the equation is true if the sum of the angles is 90º.

  13. Example 3b • Find one solution for the equation. Assume all angles involved are acute angles. (b) Since secant and cosecant are cofunctions, the equation is true if the sum of the angles is 90º.

  14. Re-Cap Write all 17 identities • Reciprocal (6) • Pythagoreans (3) • Quotients (2) • Cofunctions(6) Memorization Quiz tomorrow after warm up

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