MA 154 Lesson 14 DelworthMA 154 Lesson 14 DelworthSection 7.3 The Addition and Subtraction FormulasWe refer to the sine and cosine functions as cofunctions of each other. Similarly, the tangent and cotangent functions are cofunctions, as are the secant and cosecant. If u is the radian measure of an acute angle, then the angle with radian measure 2 u is complementary to u. If u is the degree measure of an acute angle, then the angle with degree measure 90 u is complementary to u.Express as a cofunction of a complementary angle.tan(23.54) sin(1/6)cos(/5) csc(0.74)1Cofunction Formulas:If u is a real number or the radian measure of an angle, then(1) cos2 usinu (2) sin2 ucos u(3) tan2 ucot u (4) cot2 utan u(5) sec2 ucsc u (6) csc2 usec uIf u is the degree measure of an angle, then(1) cos 90 u sinu (2) sin 90 u cosu(3) tan 90 u cot u (4) cot 90 u tan u(5) sec 90 u csc u (6) csc 90 u sec uMA 154 Lesson 14 DelworthSection 7.3 The Addition and Subtraction FormulasWe will now talk about the formulas that involve trigonometric functions of u + v or u – v for any real numbers or angles u and v. These formulas are known as addition and subtraction formulas, respectively, or as sum and difference identities. Addition and subtraction formulas for Cosine, Sine and Tangentsin(u v) sin u cosv cosu sinvsin(u v) sin ucos v cos u sin vcos(u v) cos u cos v sin u sinvcos(u v) cos u cos v sin usinvtan(u v) tan u tan v1 tan u tan vtan(u v) tan u tan v1 tan utan vFind the exact values.a) sin(2/3) + sin(/4) b) sin(11/12)(Hint: Use 11/12 = 2/3 + /4)a) tan(30) + tan (225) b) tan(255)(Hint: Use 225 = 30 +225)a) cos(/3) – cos(/4) b) cos(/12)(Hint: Use /12 = /3 – /4)2MA 154 Lesson 14 DelworthSection 7.3 The Addition and Subtraction FormulasExpress as a trigonometric function of one angle.cos17 cos25 sin17 sin25sin25 cos17 cos 25 sin17Using addition formulas to find the quadrant containing an angle.If and are acute angles such that tan158and sin1213, finda)sin b)cos c) The quadrant containing + If and are acute angles such that csc53and cot247, finda)sin b)tan c) The quadrant containing + 3MA 154 Lesson 14 DelworthSection 7.3 The Addition and Subtraction FormulasUsing addition formulas to find the quadrant containing an angle.If tan158 and sec1312 for a third-quadrant angle and second-quadrant angle , finda)sin b)tan c) The quadrant containing + 4MA 154 Lesson 14 DelworthSection 7.3 The Addition and Subtraction FormulasIf and are fourth-quadrant angles such that sec54 and cot247, finda)cos b) sinc) The quadrant containing - 5MA 154 Lesson 14 DelworthSection 7.3 The Addition and Subtraction FormulasVerify the identity:cos422cos sin tan x 4tan x 1tan x 1cos(h t) cos(h t) 2cos h cos t
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