# TRIGONOMETRY

The Domain of the Sine Function is what?

It is the set of all real numbers.

The Range of the Sine Function is what?

All real numbers from -1 to 1, inclusive.

The Domain of the Cosine Function is what?

It is the set of all real numbers

The Range of the Cosine Function is what?

All real numbers from -1 to 1, inclusive.

The Domain of the tangent function is what?

It is the set of all real numbers, except odd integer multiples of π/2 (90°).

The Range of the Tangent Function is what?

All real numbers

The Domain of the secant function is what?

It is the set of all real numbers, except odd integer multiples of π/2 (90°).

The Range of the Secant Function is what?

All real numbers greater than or equal to 1 or less than or equal to -1.

The Domain of the cotangent function is the set of what?

It is the set of all real numbers, except odd integer multiples of π (180°).

The Range of the Cotangent Function is what?

All real numbers

The Domain of the cosecant function is the set of what?

It is the set of all real numbers, except odd integer multiples of π (180°).

The Range of the cosecant function is the set of what?

All real numbers greater than or equal to 1 or less than or equal to -1.

Show the Domain of the cosecant functions and cotangent factions.....

-1 ≤ sin θ ≤ 1 and -1 ≤ tan θ ≤ 1

What is the symbol for Sine?

f ( θ ) = sin θ

sin(2A) =

2 sin A cos A

cos(2A) =

0

tan(2A) =

2 tan A/1 - tan^2 A

sin (A/2) =

+ or - Square root of 1-cosA/2

cos (A/2) =

+ or - Square root of 1 + cos A/2

tan (A/2) =

#NAME?

What is a Directed Angle?

Angles wit a terminal Ray and a initial Ray.

What is a counterclockwise rotation

This is a positive angle measure.

What is a Clockwise Rotation?

This is a negative angle measure.

One Degree equals?

This equals 60 Minutes

What does 1 minute equal?

This equals (1/60)

What does 1 Minute equal?

This Equals 60 seconds.

A Central angle of a circle is an angle whose vertex is the center.Example:

This is a unit of angle measure.One radian is equal to the measure of a central angle that intercepts and arc length of 1 radius.

Angle theta equals?

Check out page 359 of my texted.

...

s equals...?

this equals r theta which must be in radians.

360 degrees =

180 degrees =

330 degrees ---> radians (exact value)?

330 degrees X Pi rad./180 degrees = 11Pi/6

5 pi/6 rad x 180 degrees/pi rad. = 5 x 30 degrees = 150 degrees.

Sector Area is...?

A = 1/2 theta r square.

Linear speed is...?

v = s/t

Angular speed is....?

w = theta / t or

Theorem: v = rw

Proof: By 1): v = s/t = r theta/t = r(wt)/t = rw

Name the Lower Case letters in Trigonometry.

Alpha, beta gamma and theta.

What do the lower case letters Alpha, beta gamma and theta. often donate?

These lower case signs as angles.

What does it mean when the angle is said to be positive?

This means that the direction of the rotation from the initial side to the terminal side is counterclockwise.

What does it mean when the angle is said to be negative?

This means that the direction of the rotation from the initial side to the terminal side is clockwise.

This If both sides, the terminal and initial sides in either the y-axis or x-axis.

What are the two commonly used measures for angles are?

What is One degree?

it is 1/360 revolution.

What is a right angle?

It is an angle that measures 90 degrees or 1/4 revolution;

What is a straight angle?

This is an angle that measures 180 degrees or 1/2 revolution

It is customary to refer to an angle that measures what degrees?

As an angle of theta degrees.

How is one minute denoted?

1' or 1/60 degree

How is one second denoted?

1", is 1/60 minute or equivalently, 1/3600 degree.

An angle of say, 30 degrees, 40 minutes, 10 seconds is written compactly as...?

30 degree40'10

1 counterclockwise revolution =

360 degrees

What is a central angle?

This is a positive angle whose vertex is at the center of a circle.

What is the measure of an angle when the radius is r and the length of the arc subtended by the central angle is also r?

This angle would measure 1 radius.

Arc Length Theorem

For a circle of radius r, a central angle of theta radians subtends an arc whose length s is.S = r(theta)

Find the length of the arc of a circle of radius 3 meters subtended by a central angle of 0.25 radian.

Use

Area of a sector Theorem?

A = 1/2r squared = theta

Describe the Complementary Theorem.

Cofunctions of complementary angles are equal.

Finding The Width of River... et cetera:

Tan theta = b/a which leads to:Tan theta degrees = b/length of side which leads to:b = length of side times Tan theta degrees = width.

Finding the Inclination of a Mountain Trail.

Sin B = elevation height/length of trail Which leads to:B = Sin -1 elevation height/length of trail = Inclination of trail or (angle of trail)

To find the angle of a triangle what do you do.

Always look for the inverse

Finding the Heigh of a cloud?Tan Angle = 75 degreesDistance on ground from light detector to light projector = 300 feet.Height = unknown.

Must know angle of elevation of light detector and the adjacent distance to the light projector. Then you use the Tan measurement.Tan angle of light detector to degrees = h/adjacent distance from detector to the projector. = Actual distance from ground to cloud. Tan 75 = h/300 ----> 300 tan 75 = h = approx. 1120 feet.