Others Flashcards
What is the definition of a right triangle?
A triangle that has one angle measuring 90 degrees.
True or False: The sine of an angle in a right triangle is the ratio of the opposite side to the hypotenuse.
True
What is the hypotenuse in a right triangle?
The side opposite the right angle, and the longest side of the triangle.
Fill in the blank: The cosine of an angle is the ratio of the ______ side to the hypotenuse.
adjacent
What is the Pythagorean theorem?
In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
What are the primary trigonometric ratios?
Sine, Cosine, and Tangent.
True or False: The tangent of an angle is the ratio of the adjacent side to the opposite side.
False
What is the formula for sine in a right triangle?
sin(θ) = opposite/hypotenuse
What is the formula for cosine in a right triangle?
cos(θ) = adjacent/hypotenuse
What is the formula for tangent in a right triangle?
tan(θ) = opposite/adjacent
Fill in the blank: The reciprocal of sine is called ______.
cosecant
Fill in the blank: The reciprocal of cosine is called ______.
secant
Fill in the blank: The reciprocal of tangent is called ______.
cotangent
What is the value of sin(90°)?
1
What is the value of cos(0°)?
1
What is the value of tan(45°)?
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 unit circle?
A circle with a radius of 1 centered at the origin of the coordinate plane.
What are the coordinates of the point on the unit circle at 0 radians?
(1, 0)
What are the coordinates of the point on the unit circle at π/2 radians?
(0, 1)
What is the sine of 30 degrees?
1/2
What is the cosine of 60 degrees?
1/2
What is the tangent of 30 degrees?
√3/3
What is the tangent of 60 degrees?
√3
Fill in the blank: The angle whose sine is 0 is ______.
0° or 180°
Fill in the blank: The angle whose cosine is 0 is ______.
90° or 270°
What is the relationship between sine and cosine?
sin(θ) = cos(90° - θ)
What is the sine addition formula?
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
What is the cosine addition formula?
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
What is the range of the sine function?
-1 to 1
What is the range of the cosine function?
-1 to 1
What is the range of the tangent function?
All real numbers
What is an angle in standard position?
An angle whose vertex is at the origin and whose initial side lies along the positive x-axis.
What is the reference angle?
The acute angle formed by the terminal side of the angle and the x-axis.
True or False: The reference angle is always positive.
True
What is the relationship between degrees and radians?
180 degrees is equal to π radians.
Convert 90 degrees to radians.
π/2 radians
Convert 180 degrees to radians.
π radians
Convert 360 degrees to radians.
2π radians
What is a periodic function?
A function that repeats its values at regular intervals.
What is the period of the sine function?
2π
What is the period of the cosine function?
2π
What is the period of the tangent function?
π
What is an amplitude?
The maximum distance from the midline of a wave to its peak.
What is the amplitude of the sine function?
1
What is the amplitude of the cosine function?
1
What is a trigonometric identity?
An equation that is true for all values of the variable.
What is the Pythagorean identity?
sin²(θ) + cos²(θ) = 1
What is the definition of an angle?
A figure formed by two rays, called the sides of the angle, sharing a common endpoint called the vertex.
What is the vertex of an angle?
The common endpoint where the two rays meet.
What is a complementary angle?
Two angles that add up to 90 degrees.
What is a supplementary angle?
Two angles that add up to 180 degrees.
