Formule trigonometrice Flashcards
sin cos tg ctg (27 cards)
What is the sine of an angle in a right triangle?
The ratio of the length of the opposite side to the length of the hypotenuse.
What is the cosine of an angle in a right triangle?
The ratio of the length of the adjacent side to the length of the hypotenuse.
What is the tangent of an angle in a right triangle?
The ratio of the length of the opposite side to the length of the adjacent side.
True or False: The sine function is defined for all real numbers.
True
Fill in the blank: The formula for the Pythagorean theorem is ______.
a² + b² = c²
What is the formula for the sine of the sum of two angles?
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
What is the formula for the cosine of the difference of two angles?
cos(a - b) = cos(a)cos(b) + sin(a)sin(b)
What is the secant function?
The reciprocal of the cosine function, sec(x) = 1/cos(x).
What is the cosecant function?
The reciprocal of the sine function, csc(x) = 1/sin(x).
What is the cotangent function?
The reciprocal of the tangent function, cot(x) = 1/tan(x).
What is the relationship between the sine and cosine of complementary angles?
sin(90° - x) = cos(x).
True or False: tan(x) = sin(x)/cos(x).
True
Fill in the blank: The double angle formula for sine is ______.
sin(2x) = 2sin(x)cos(x)
What is the double angle formula for cosine?
cos(2x) = cos²(x) - sin²(x)
What is the range of the sine function?
The range is [-1, 1].
What is the range of the cosine function?
The range is [-1, 1].
What is the formula for converting radians to degrees?
Degrees = Radians × (180/π).
What is the formula for converting degrees to radians?
Radians = Degrees × (π/180).
What is the sine of 30 degrees?
1/2
What is the cosine of 60 degrees?
1/2
What is the tangent of 45 degrees?
1
What is the law of sines?
a/sin(A) = b/sin(B) = c/sin(C)
What is the law of cosines?
c² = a² + b² - 2ab*cos(C)
True or False: The unit circle defines the sine and cosine functions.
True
