# ws_1 - -1(sin π 12 sin-1(sin 2 π 3 6 Find the exact value...

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Mathematics for Engineers I (Math103). .. student-intranet/faculties/math/ 2008 - Fall/math103 Class Work Sheet 1. 1. Graph each of the following polynomials and rational functions, then from the graph ﬁnd its domain and range. (i) f ( x ) = ( x - 1) 2 + 3. (ii) f ( x ) = 2 x + 3. (iii) f ( x ) = x 2 + 2 x . (iv) f ( x ) = 3( x + 2) 2 - 1. (v) f ( x ) = 3 x +2 . (vi) f ( x ) = - 1 ( x - 1) 2 + 2. 2. Graph each of the following functions. Find the period in each case. (i) y = sin( x 2 ). (ii) y = -| cos(2 πx ) | . (iii) y = sin( x + π 2 ). (iv) y = cos( x + π 4 ) - 1. (v) y = sin(2 x + π ). 3. Evaluate:(Using the basic identities). (i) sin( 7 π 12 ) as sin( π 4 + π 3 ). (ii) cos( 11 π 12 ) as cos( π 4 + 2 π 3 ). (iii) cos( π 12 ). (iv) sin( 5 π 12 ). (v) cos 2 ( π 8 ). (vi) cos 2 ( π 12 ). (vii) sin 2 ( π 8 ). 4. Solve the following equations. (i) x 2 - 2 x - 3 = 0. (ii) x +2 x 2 + x +1 = 0. (iii) x - 1 x 2 - 2 x +1 = 0. (iv) sin 2 (3 x ) + cos 2 (3 x ) = 1. (v) sin(2 x ) = 1 where x [0 , 2 π ]. (vi) cos(3 x ) = 0 where x [0 , 2 π ]. (vii) | sin( x ) | = 1 where x [0 , 2 π ]. (viii) cos 2 ( x ) - cos( x ) - 2 = 0 where x [0 , 2 π ]. 1

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5. Evaluate: sin(sin - 1 (0 . 6)) ; sin
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Unformatted text preview: -1 (sin( π 12 )) ; sin-1 (sin( 2 π 3 )) . 6. Find the exact value of: (i) cos-1 (-1). (ii) arctan(-1). (iii) csc-1 (2). (iv) sec-1 ( √ 2). (v) arccos(cos(2 π )). (vi) tan(sin-1 ( 2 3 )). (vii) csc(arccos( 3 5 )). (viii) cos(tan-1 (2) + tan-1 (3)). (ix) sin(2tan-1 ( √ 2)). 7. Simplify the expression (i) tan(sin-1 x ). (ii) csc(arctan(2 x )). (iii) sin(tan-1 x ). (iv) sin(tan-1 ( √ x 2-2 x )), x ≥ 2. 8. Prove that for xy 6 = 1; tan-1 x + tan-1 y = tan-1 x + y 1-xy , if the left hand side lies between-π 2 and π 2 . 9. Given α = sin-1 ( 5 13 ). Find the value of all trigonometric functions of α . 10. Given α = sec-1 (-√ 5). Find the value of all trigonometric functions of α . 2...
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## This note was uploaded on 01/08/2010 for the course MATH Math103 taught by Professor Dr.prof.mostafaamer during the Winter '09 term at German University in Cairo.

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ws_1 - -1(sin π 12 sin-1(sin 2 π 3 6 Find the exact value...

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