Unit Circle
What is a Unit Circle?
a circle with a radius of 1 centered at the origin of a coordinate plane.
What is the definition of the sine ratio?
The sine ratio is the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.
What is the equation to find the sine of an angle?
sin(angle) = opposite/hypotenuse.
What is a reference angle?
A reference angle is the positive acute angle between the terminal side of an angle in standard position and the x-axis.
What is the pythagorean identity?
the square of the sine of the angle plus the square of the cosine of the angle equals 1.
What are the coordinates of the point on the Unit Circle corresponding to an angle of 90 degrees?
The coordinates of the point are (0, 1).
What is the value of the cosine ratio for a right angle?
The value of the cosine ratio for a right angle is O.
What is the equation to find the cosine of an angle?
cos(angle) = adjacent/hypotenuse.
How do you find the reference angle for a given angle?
To find the reference angle for a given angle: 1. Determine the angle's position relative to the x-axis. 2. If the angle is in the first or second quadrant, the reference angle is equal to the angle itself. 3. If the angle is in the third or fourth quadrant, subtract the angle from 180 degrees (or n radians) to find the reference angle.
What is the reciprocal identity?
the cosecant angle is equal to 1 divided by the sine of the angle.
What is the trigonometric function for the x-coordinate of a point on the Unit Circle?
The x-coordinate corresponds to the cosine function.
What is the tangent ratio equal to?
The tangent ratio is equal to the ratio of the sine to the cosine of an angle in a right triangle.
What is the equation to find the tangent of an angle?
tan(angle) = opposite/adjacent.
Can the reference angle be negative?
No, the reference angle is always a positive acute angle.
What is the quotient identity?
the tangent of the angle is equal to the sine of the angle divided by the cosine of the angle.
What is the value of the sine function for an angle of 30 degrees on the Unit Circle?
The value is 0.5.
What is the value of the sine ratio for a 45-degree angle in a right triangle?
The value of the sine ratio for a 45-degree angle is V2/2.
How do you solve the equation sin(x) = O?
To solve sin(x) = 0, you find the angles where the sine function equals zero, which are 0°, 180°, 360°, and so on.
What is the relationship between a given angle and its reference angle?
The reference angle is always smaller than or equal to the given angle. They are related through the acute angle formed with the x-axis.
What is the co-function identity for cosine?
the cosine of the angle, is equal to the sine of the complimentary angle.
What is the reference angle for an angle of 225 degrees on the Unit Circle?
The reference angle is 45 degrees.
What is the reciprocal of the cosine ratio?
The reciprocal of the cosine ratio is the secant ratio.
What are the solutions to the equation cos(x) = 1/2?
The solutions to cos(x) = 1/2 are x = 60° and x = 300°.
Why do we use reference angles?
Reference angles simplify trigonometric calculations and allow us to work with positive angles in all four quadrants.
What is the double-angle identity for sine?
the sine of twice the angle is equal to 2 times the sine of the angle times the cosine of the angle.