Turn-In Assignment: Trigonometric Identities Part II Show all work using Microsoft Equation editor in WORD Task 1: Refreshing fundamental identities learned in section 6.1 Turn in Exercise Set 6.1 Problems 31, 35 (Page 651) 31.) cos x 1sin x + =2 sec x 1sin x cos x 35.) sec xcsc x tan x1 = sec x+ csc x tan x +1 Task 2: Critical thinking exercise on Sum - Difference formula 1. Answer each of the following questions: a) sin 30 b) sin 60 = ? c) sin 30 d) sin(30+ 60) =? + sin 60 = ? (simplify) = sin 90 =? e) Does sin 30 + sin 60 equal sin(30+ 60) f) Based upon your answers for (a) - (e), do you think sin y is ALWAYS true? Justify your answer. M5_Learning_Module_Trig_Identities ? Answer Yes or No sin(x + y ) = sin x + Trig Identities 2. Do you think cos( x+ y ) = cos x Page 2 of 3 + cos y is ALWAYS true? Justify your answer. (Hint: One way is to follow the steps (a) - (e) in the above problem, replacing Sine with Cosine. There are other ways, too. Be creative! ) Task 3: Applying sum/difference formulas for sine, cosine and tangent (Page 661) Turn in Exercise Set 6.2, Problems 10, 17, 19, 31, 38, 40, 61(b), 63(c) (Page 661) Hint for 61(b) and 63(c): Quadrant info is super important Instructions: While solving the above problems, show each step. Otherwise, points will be deducted. For question 10, verify and name the identity: cos ( ) 10.) sin sin =cot a cot +1 For question 17 and 19, find the exact value of each expression: 17.) cos( 135 +30 ) 19.) cos 75 For question 31, write each expression as the sine, cosine, or tangent of an angle. Then find the exact value of the expression: 31.) tan tan 5 30 1+ tan tan 5 30 For question 38 and 40, verify each identity, name the identity: 38.) tan ( x )=tan x 40.) cos ( + )+ cos ( )=2 cos cos . Trig Identities Page 3 of 3 For questions 61 and 63, find the exact value of the following under the given conditions: 8 1 61.) cos a= 17 , a liesquadrant IV ,sin = 2 , lies quadrant III . 63.) 3 3 1 3 tan = , < < ,cos = , < < 2 4 2 4 2 For questions 61 and 63, find the exact value of the following under the given conditions: 8 1 61.) cos a= 17 , a liesquadrant IV ,sin = 2 , lies quadrant III . 63.) 3 3 1 3 tan = , < < ,cos = , < < 2 4 2 4 2 M5_Learning_Module_Trig_Identities \fFor questions 61 and 63, find the exact value of the following under the given conditions: 8 1 61.) cos a= 17 , a liesquadrant IV ,sin = 2 , lies quadrant III . 63.) 3 3 1 3 tan = , < < ,cos = , < < 2 4 2 4 2 M5_Learning_Module_Trig_Identities \f