Trigonometry Identities Flashcards
What is the Pythagorean identity for sine and cosine?
sin²(x) + cos²(x) = 1
True or False: tan(x) is equal to sin(x) / cos(x).
True
What is the identity for cotangent in terms of sine and cosine?
cot(x) = cos(x) / sin(x)
Fill in the blank: The double angle formula for sine is sin(2x) = _____ .
2sin(x)cos(x)
What is the sum of angles formula for cosine?
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
What is the value of sin(90°)?
1
True or False: sec(x) is the reciprocal of cos(x).
True
What is the formula for the tangent of a sum of angles?
tan(a + b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b))
Fill in the blank: The double angle formula for cosine is cos(2x) = _____ .
cos²(x) - sin²(x)
What is the identity for cosecant in terms of sine?
csc(x) = 1 / sin(x)
What is the formula for the sine of a difference of angles?
sin(a - b) = sin(a)cos(b) - cos(a)sin(b)
True or False: sin(-x) = -sin(x).
True
What is the value of cos(0°)?
1
What is the cofunction identity for sine and cosine?
sin(x) = cos(90° - x)
Fill in the blank: The identity for secant in terms of cosine is sec(x) = _____ .
1 / cos(x)
What is the relationship between cosecant and sine?
csc(x) = 1 / sin(x)
What is the formula for the sine of a sum of angles?
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
True or False: cos(-x) = cos(x).
True
What is the formula for cotangent in terms of tangent?
cot(x) = 1 / tan(x)
Fill in the blank: The identity for tangent in terms of sine and cosine is tan(x) = _____ .
sin(x) / cos(x)
What is the identity for the tangent of a difference of angles?
tan(a - b) = (tan(a) - tan(b)) / (1 + tan(a)tan(b))
What is the value of tan(45°)?
1
True or False: All trigonometric functions are periodic.
True
What is the period of the sine function?
2π
