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))"
}
]
}