Trig Idenites

{

"flashcards": [

{

"question": "What is the reciprocal identity for sin(x)?",

"answer": "sin(x) = 1/csc(x)"

},

{

"question": "What is the Pythagorean identity for sin(x) and cos(x)?",

"answer": "sin^2(x) + cos^2(x) = 1"

},

{

"question": "What is the double-angle formula for sin(2x)?",

"answer": "sin(2x) = 2sin(x)cos(x)"

},

{

"question": "What is the double-angle formula for cos(2x)?",

"answer": "cos(2x) = cos^2(x) - sin^2(x)"

},

{

"question": "What is the product-to-sum formula for sin(x)cos(y)?",

"answer": "sin(x)cos(y) = 1/2[sin(x+y) + sin(x-y)]"

},

{

"question": "What is the half-angle formula for sin^2(x)?",

"answer": "sin^2(x) = (1 - cos(2x))/2"

},

{

"question": "What is the derivative of arcsin(x)?",

"answer": "d/dx[arcsin(x)] = 1/sqrt(1-x^2)"

},

{

"question": "What is the Pythagorean identity involving tan(x)?",

"answer": "1 + tan^2(x) = sec^2(x)"

},

{

"question": "What is the sum formula for sin(x + y)?",

"answer": "sin(x + y) = sin(x)cos(y) + cos(x)sin(y)"

},

{

"question": "What is the sum formula for cos(x + y)?",

"answer": "cos(x + y) = cos(x)cos(y) - sin(x)sin(y)"

},

{

"question": "What is the double-angle formula for tan(2x)?",

"answer": "tan(2x) = 2tan(x)/(1 - tan^2(x))"

}

]

}