Trigonometry Flashcards
Practice (28 cards)
What is the sine of an angle in a right triangle?
The ratio of the length of the opposite side to the hypotenuse.
What is the cosine of an angle in a right triangle?
The ratio of the length of the adjacent side to 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.
What is the formula for the sine function?
sin(θ) = opposite / hypotenuse
What is the formula for the cosine function?
cos(θ) = adjacent / hypotenuse
What is the formula for the tangent function?
tan(θ) = opposite / adjacent
True or False: The tangent function can be expressed as the ratio of sine and cosine.
True
What is the Pythagorean identity?
sin²(θ) + cos²(θ) = 1
What is the reciprocal of the sine function?
Cosecant (csc), where csc(θ) = 1/sin(θ)
What is the reciprocal of the cosine function?
Secant (sec), where sec(θ) = 1/cos(θ)
What is the reciprocal of the tangent function?
Cotangent (cot), where cot(θ) = 1/tan(θ)
Fill in the blank: The sine of 90 degrees is _____
1
Fill in the blank: The cosine of 0 degrees is _____
1
What are the angles for which sine and cosine are equal?
45 degrees (π/4 radians) and 225 degrees (5π/4 radians)
What is the value of tan(45 degrees)?
1
True or False: The sine function is an odd function.
True
True or False: The cosine function is an even function.
True
What is the formula for converting degrees to radians?
Radians = Degrees × (π/180)
What is the angle in radians for 90 degrees?
π/2 radians
What is the angle in radians for 180 degrees?
π radians
Fill in the blank: The sine of 0 degrees is _____
0
What is the value of cos(90 degrees)?
0
What is the relationship between sine and cosine in the unit circle?
The x-coordinate is the cosine value and the y-coordinate is the sine value.
What is the range of the sine function?
[-1, 1]
