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