Trigonometry – Trigonometric Equations Review Questions

Trigonometry – Trigonometric Equations Review Questions -...

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Trigonometry – Trigonometric Equations Review Questions Problem : Solve the following equation: sin( x )tan( x ) = 0 . Solving sin( x ) = 0 , x = 0, Π . Solving tan( x ) = 0 , the same solutions are reached. x = 0, Π . Problem : Solve the following equation: cos( x ) - tan 2 ( x ) = 1 . Using the identity 1 + tan 2 ( x ) = sec 2 ( x ) , the equation cos 3 ( x ) = 1 results. Therefore cos( x ) = 1 , and x = 0 . Problem : Solve the following equation: sin 2 ( x ) - 1 = cos 2 ( x ) + 2 . Using the identity sin 2 ( x ) + cos 2 ( x ) = 1 , the equation sin 2 ( x ) = 2 results. This equation has no solution. Problem : Solve the following equation: 2 sec( x )sin 3 ( x ) = cos( x )tan 2 ( x ) . Resolving everything into sines and cosines and then cancelling, we have sin( x ) = . x = , . Problem : Solve the following equation: sin( x ) + sin( x )cot 2 ( x ) = sec 2 ( x ) - tan 2 ( x ) . Factoring on the right side and the use of identities leads to the equations sin( x ) = 1 . Therefore, x = . Problem : What is arccos( ) ? +2 , +2 , where n is an integer. Problem : What is arcsin(0) , where n is an integer. Problem : What is arccos( ) ? There is no solution, because there exists no angle whose cosine > 1 .
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