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# More Trigonometric Identities

## Contents

#### Problems

Problem : Use α = 30 o and β = 45 o to find the sine, cosine, and tangent of 75 o .

sin(75 o ) = sin(30 o +45 o ) = sin(30 o )cos(45 o ) + cos(30 o )sin(45 o ) 0.9659 . cos(75 o ) = cos(30 o +45 o ) = cos(30 o )cos(45 o ) - sin(30 o )sin(45 o ) 0.2588 . tan(75 o ) = tan(30 o +45 o ) = 3.732 .

Problem : Use α = 135 o and β = 30 o to find the sine, cosine, and tangent of 105 o .

sin(105 o ) = sin(135 o -30 o ) = sin(135 o )cos(30 o ) - cos(135 o )sin(30 o ) 0.9659 . cos(105 o ) = cos(135 o -30 o ) = cos(135 o )cos(30 o ) + sin(135 o )sin(30 o ) - 0.2588 . tan(105 o ) = tan(135 o -30 o ) = - 3.732 .

Problem : Express the following as a function of a single angle: sin(20 o )sin(30 o ) + cos(20 o )cos(30 o ) .

cos(- 10 o )

Problem : Express the following as a function of a single angle: .

tan(72 o )

Problem : Express the following as a function of a single angle: sin(340 o )cos(120 o ) + cos(340 o )sin(120 o ) .

sin(460 o ) = sin(100 o ) .