Trigonometry

Higher Mathematics Unit 2 – Mathematics 26. Solve 2 cos2x = 1 where 0 ≤ x ≤ π .cos2x = 1 π − 2x2x2S A ̌T C ̌2 x = π or 2π− π4 4or 2π+ π42 x = π or7π4 4x = π 78 or π87. Solve24cos x = 3 where 0 < x < 2π.( cos x ) 2 = 34cos x = ± 34cos x = ±32π + 2x2π− 2x2x= cos= π4−( )1 120 ≤ x ≤ π0 ≤ 2x≤ 2π̌ S A ̌ Since cos x can be positive or negativě T C ̌x = cos= π6−( )1 32x = π6or π − π6or π + π6or 2π− π6or 2π+ π6x = π 5 7 116orπ6orπ6or π68. Solve 3tan( 3x° − 20° ) = 5 where 0 ≤ x ≤ 360 .3tan( 3x° − 20° ) = 5tan( 3x° − 20° ) = 53S A ̌̌ T C0 ≤ x ≤ 3600 ≤ 3x≤1080−20 ≤ 3x− 20 ≤1060( )−1 3x− 20 = tan53= 59·036 (to 3 d.p.)3x − 20 = 59·036 or 180 + 59·036or 360 + 59·036 or 360 + 180 + 59·036or 360 + 360 + 59·036 or 360 + 360 + 180 + 59·036or 360 + 360 + 360 + 59·0362π31π632π41π41hsn.uk.netPage 92HSN22300