Trig Flashcards
(25 cards)
What is the Pythagorean identity?
sin²(x) + cos²(x) = 1
True or False: tan(x) = sin(x) / cos(x).
True
Fill in the blank: The identity for sin(2x) is ____.
2sin(x)cos(x)
What is the double angle formula for cos(2x)?
cos(2x) = cos²(x) - sin²(x)
Which identity expresses tan(2x) in terms of tan(x)?
tan(2x) = 2tan(x) / (1 - tan²(x))
What is the co-function identity for sin?
sin(x) = cos(90° - x)
True or False: The identity for sec(x) is 1/cos(x).
True
What is the identity for cot(x) in terms of sin and cos?
cot(x) = cos(x) / sin(x)
Fill in the blank: The identity for cos(2x) can also be expressed as ____.
1 - 2sin²(x)
What is the sum of angles formula for sin?
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
What is the difference of angles formula for cos?
cos(a - b) = cos(a)cos(b) + sin(a)sin(b)
True or False: sin(-x) = -sin(x).
True
What is the identity for csc(x)?
csc(x) = 1/sin(x)
Fill in the blank: The identity for sin(3x) is ____.
3sin(x) - 4sin³(x)
What is the product-to-sum formula for sin(x)sin(y)?
sin(x)sin(y) = 1/2 [cos(x - y) - cos(x + y)]
What is the sum of angles formula for tan?
tan(a + b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b))
True or False: cos(-x) = cos(x).
True
What is the identity for sec(2x)?
sec(2x) = 1/cos(2x)
Fill in the blank: The identity for tan(3x) is ____.
3tan(x) - tan³(x) / (1 - 3tan²(x))
What is the co-function identity for cos?
cos(x) = sin(90° - x)
What is the identity for sin(a + b)?
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
What is the identity for cot(2x)?
cot(2x) = (1 - tan²(x)) / (2tan(x))
True or False: All trigonometric identities can be derived from the Pythagorean identity.
True
What is the product-to-sum formula for cos(x)cos(y)?
cos(x)cos(y) = 1/2 [cos(x + y) + cos(x - y)]
