More Trigonometric Identities

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

Solution for Problem 1 >>

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 .

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

Solution for Problem 2 >>

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 .

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

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

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