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A 23-ft ladder leans against a building so that the angle between the ground and the ladder is 80° . How high does the ladder reach up the side of the building?

22.6506 ft

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The angle of elevation to the top of a building in New York is found to be 9 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building.

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The angle of elevation to the top of a building in Seattle is found to be 2 degrees from the ground at a distance of 2 miles from the base of the building. Using this information, find the height of the building.

368.7633 ft

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Assuming that a 370-foot tall giant redwood grows vertically, if I walk a certain distance from the tree and measure the angle of elevation to the top of the tree to be 60° , how far from the base of the tree am I?

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Review exercises

Angles

For the following exercises, convert the angle measures to degrees.

For the following exercises, convert the angle measures to radians.

Find the length of an arc in a circle of radius 7 meters subtended by the central angle of 85°.

10.385 meters

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Find the area of the sector of a circle with diameter 32 feet and an angle of 3 π 5 radians.

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For the following exercises, find the angle between 0° and 360° that is coterminal with the given angle.

For the following exercises, find the angle between 0 and 2 π in radians that is coterminal with the given angle.

20 π 11

2 π 11

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For the following exercises, draw the angle provided in standard position on the Cartesian plane.

Find the linear speed of a point on the equator of the earth if the earth has a radius of 3,960 miles and the earth rotates on its axis every 24 hours. Express answer in miles per hour.

1036.73 miles per hour

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A car wheel with a diameter of 18 inches spins at the rate of 10 revolutions per second. What is the car's speed in miles per hour?

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Unit Circle: Sine and Cosine Functions

Find the exact value of sin π 3 .

3 2

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Find the exact value of cos π 4 .

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Find the exact value of cos π .

–1

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State the reference angle for 300° .

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State the reference angle for 3 π 4 .

π 4

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Compute cosine of 330° .

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Compute sine of 5 π 4 .

2 2

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State the domain of the sine and cosine functions.

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State the range of the sine and cosine functions.

[ 1 , 1 ]

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The Other Trigonometric Functions

For the following exercises, find the exact value of the given expression.

For the following exercises, use reference angles to evaluate the given expression.

If sec ( t ) = 2.5 , what is the sec ( t ) ?

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If tan ( t ) = 0.6 , what is the tan ( t ) ?

0.6

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If tan ( t ) = 1 3 , find tan ( t π ) .

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If cos ( t ) = 2 2 , find sin ( t + 2 π ) .

2 2 or 2 2

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Which trigonometric functions are even?

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Which trigonometric functions are odd?

sine, cosecant, tangent, cotangent

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Right Triangle Trigonometry

For the following exercises, use side lengths to evaluate.

cos ( π 2 ) = sin ( __° )

0

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csc ( 18 ° ) = sec ( __° )

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For the following exercises, use the given information to find the lengths of the other two sides of the right triangle.

cos B = 3 5 , a = 6

b = 8 , c = 10

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For the following exercises, use [link] to evaluate each trigonometric function.

A right triangle with side lengths of 11 and 6. Corners A and B are also labeled.

For the following exercises, solve for the unknown sides of the given triangle.

A 15-ft ladder leans against a building so that the angle between the ground and the ladder is 70° . How high does the ladder reach up the side of the building?

14.0954 ft

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The angle of elevation to the top of a building in Baltimore is found to be 4 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building.

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Practice test

Convert 5 π 6 radians to degrees.

150°

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Convert −620° to radians.

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Find the length of a circular arc with a radius 12 centimeters subtended by the central angle of 30° .

6.283 centimeters

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Find the area of the sector with radius of 8 feet and an angle of 5 π 4 radians.

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Find the angle between and 360° that is coterminal with 375° .

15°

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Find the angle between 0 and 2 π in radians that is coterminal with 4 π 7 .

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Draw the angle 315° in standard position on the Cartesian plane.

A graph of a circle with an angle inscribed.
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Draw the angle π 6 in standard position on the Cartesian plane.

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A carnival has a Ferris wheel with a diameter of 80 feet. The time for the Ferris wheel to make one revolution is 75 seconds. What is the linear speed in feet per second of a point on the Ferris wheel? What is the angular speed in radians per second?

3.351 feet per second, 2 π 75 radians per second

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Find the exact value of sin π 6 .

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Compute sine of 240° .

3 2

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State the domain of the sine and cosine functions.

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State the range of the sine and cosine functions.

[ 1 , 1 ]

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Find the exact value of cot π 4 .

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Find the exact value of tan π 3 .

3

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Use reference angles to evaluate csc 7 π 4 .

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Use reference angles to evaluate tan 210 ° .

3 3

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If csc t = 0.68 , what is the csc ( t ) ?

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If cos t = 3 2 , find cos ( t 2 π ) .

3 2

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Which trigonometric functions are even?

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Find the missing angle: cos ( π 6 ) = sin ( ___ )

π 3

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Find the missing sides of the triangle A B C : sin B = 3 4 , c = 12

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Find the missing sides of the triangle.

A right triangle with hyptenuse length of 9 and angle measure of 60 degrees.

a = 9 2 , b = 9 3 2

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The angle of elevation to the top of a building in Chicago is found to be 9 degrees from the ground at a distance of 2000 feet from the base of the building. Using this information, find the height of the building.

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Questions & Answers

how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
which site have a normal flora
ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
Safaa
skin
Asiina
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
all
Tesfaye
by fussion
Asiina
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
what is inflammation
Shelly Reply
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Micheal Reply
Binomial nomenclature
adeolu
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Source:  OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
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