Chapter 1: The Six Trigonometric Functions
1/cos(theta)
What is the reciprocal identity for sec(theta)?
sin²(theta)
What is the shorthand notation for (sin(theta))²?
Absolute Value Signs
What must be used when taking the square root of a trigonometric function if you don't know if it is positive or negative?
Circle, Radius, Center
A _______ is the set of all points in the plane that are a fixed distance from a given fixed point. The fixed distance is the ______. The fixed point is the ______. Separate with comma.
Triangle
A three sided polygon.
r/y
According to Definition 1, cosecant of theta equals:
x/r
According to Definition 1, cosine of theta equals:
x/y
According to Definition 1, cotangent of theta equals:
y/r
According to Definition 1, sin of theta equals:
y/x
According to Definition 1, tangent of theta equals:
r/x
According to definition 1, secant of theta equals:
Angle
An _____ is formed by two rays with the same end point.
Obtuse, Right
An _____ triangle has exactly one obtuse angle, and a ______ triangle has one right angle. Separate with commas.
Isosceles
An ______ triangle has two equal sides and two equal angles.
Standard Position
An angle is said to be in __________ ________ if its initial side is along the positive x-axis and its vertex is at the origin.
Straight
Angles that measure 180 degrees are called _____ angles.
Right
Angles that measure 90 degrees are called _____ angles.
Acute
Angles that measure between 0 degrees and 90 degrees are called ____ angles.
Obtuse
Angles that measure between 90 degrees and 180 degrees are called _____ angles.
y=a(x-h)²+k
Any parabola that opens up or down can be described by an equation with the form: __________. The highest/lowest point, or vertex is denoted by the coordinates, (h,k), and a determines how wide and what direction the parabola opens.
Slope, Intercept
Every nonvertical straight line (geometric concept) can be paired with an equation of the form y = mx + b (an algebraic concept). If it is written like this, the form is called ______-______ form. Separate with a comma.
Three
Every triangle has ___ sides and ___ angles. Type the word once.
Scalene
If all the sides and angles are different, the triangle is called _______.
Quadrantal Angle
If the terminal side of an angle in standard position lies along one of the axes, it is called a _________ _________.
45
If the two acute angles in a right triangle are both ___ degrees, then the two shorter sides (the legs) are equal and the longest side (the hypotenuse) is √2 times as long as the shorter sides.
Definition I
If theta is an angle in standard position and the point (x,y) is any point on the terminal side of theta other than the origin, then the six trigonometric functions of angle theta are defined as: the sine of theta = y/r the cosine of theta = x/r the tangent of theta = y/x the cotangent of theta = x/y the secant of theta = r/x the cosecant of theta = r/y where x²+y²=r² or r=√x²+y². that is, r is the distance from the origin to (x,y)
Complementary, Complement
If two angles have a sum of 90 degrees, then they are called _____ angles, and we say each is the ______ of the other. Separate with commas.
Acute
In an ______ triangle, all three angles are acute.
Equilateral
In an ______ triangle, all three sides are of equal length and all three angles are equal.
Half
In any right triangle in which the two acute angles are 30 degrees and 60 degrees, the shortest side is always ____ the longest side (hypotenuse), and the side of medium length (the side opposite the angle) is always √3 times the shortest side. Separate with a dash (-).
30-60
In any right triangle in which the two acute angles are ____ degrees and _____ degrees, the shortest side is always half the longest side (hypotenuse), and the side of medium length (the side opposite the angle) is always √3 times the shortest side. Separate with a dash (-).
Hypotenuse
In every right triangle, the longest side is called the _____, and it is always opposite the right angle
Opposite
It is a standard practice in mathematics to label the corresponding sides _____ the angles.
Degrees
One way to measure the size of an angle is with ________.
Cartesian
The Rectangular (_____________) Coordinate System has two axes that divide the plane into four quadrants.
Unit
The _____ circle has a radius of 1.
360
The angle formed by rotating a ray through one complete revolution has a measure of ___ degrees.
Vertex, Sides
The common end point is called the _____ of the angle, and the rays are called the _____ of the angle. Separate with comma.
sqrt
The distance between any two points (x, y) and (x₂, y₂) in a rectangular coordinate system is given by the formula: r = ________ (x₂-x₁)²+(y₂-y₁)²
(x-h)²+(y-k)²=r²
The equation of a circle with center (h,k) and radius r>0 is given by the formula: __________________.
Counterclockwise
The four quadrents are numbered I to IV in a _____________________ direction.
Legs
The other two shorter sides are called the _____ of the right triangle.
Terminal Side
The side an angle rotates to is called the ____________ ________.
Initial Side
The side where the angle starts is called the ________ ________.
180
The sum of the angles in any triangle is _____˚.
Complementary
The two angles in a right triangle (other than the 90 degree) must be, _________, acute angles
False
True or False? Similar Triangles are proportional, so their trig functions are not similar as well.
Coterminal Angles
Two angles in standard position with the same terminal side are called _________ _______.
Supplementary
Two angles with a sum of 180 degrees are called _______ angles.
Uppercase, Lowercase
We denote the angles (or vertices) of a triangle with _____ letters and the lengths of the sides with _____ letters. Separate with commas.
Sin and Csc
What is positive in QI and QII
Tan and Cot
What is positive in QI and QIII
Cos and Sec
What is positive in QI and QIV?
cos²(theta)+sin²(theta)=1
What is the First Pythagorean identity?
1+tan²(theta)=sec²(theta)
What is the Second Pythagorean Identity?
1+cot²(theta)=csc²(theta)
What is the Third Pythagorean Identity?
cos(theta)/sin(theta)
What is the ratio identity for cot(theta)?
sin(theta)/cos(theta)
What is the ratio identity for tan(theta)?
1/tan(theta)
What is the reciprocal identity for cot(theta)?
1/sin(theta)
What is the reciprocal identity for csc(theta)?
Negative
When the rotation from the initial side to the terminal side takes place in a clockwise direction, the angle formed is considered a _______ angle.
Positive
When the rotation from the initial side to the terminal side takes place in a counterclockwise direction, the angle formed is considered a _______ angle.
+
c² = a² ____ b²