<< Chapter < Page Chapter >> Page >

6 tan 2 x + 13 tan x = −6

Got questions? Get instant answers now!

tan 2 x sec x = 1

1.0472 , 3.1416 , 5.2360

Got questions? Get instant answers now!

sin 2 x 2 cos 2 x = 0

Got questions? Get instant answers now!

2 tan 2 x + 9 tan x 6 = 0

0.5326 , 1.7648 , 3.6742 , 4.9064

Got questions? Get instant answers now!

4 sin 2 x + sin ( 2 x ) sec x 3 = 0

Got questions? Get instant answers now!

Extensions

For the following exercises, find all solutions exactly to the equations on the interval [ 0 , 2 π ) .

csc 2 x 3 csc x 4 = 0

sin 1 ( 1 4 ) , π sin 1 ( 1 4 ) , 3 π 2

Got questions? Get instant answers now!

sin 2 x cos 2 x 1 = 0

Got questions? Get instant answers now!

sin 2 x ( 1 sin 2 x ) + cos 2 x ( 1 sin 2 x ) = 0

π 2 , 3 π 2

Got questions? Get instant answers now!

3 sec 2 x + 2 + sin 2 x tan 2 x + cos 2 x = 0

Got questions? Get instant answers now!

sin 2 x 1 + 2 cos ( 2 x ) cos 2 x = 1

There are no solutions.

Got questions? Get instant answers now!

tan 2 x 1 sec 3 x cos x = 0

Got questions? Get instant answers now!

sin ( 2 x ) sec 2 x = 0

0 , π 2 , π , 3 π 2

Got questions? Get instant answers now!

sin ( 2 x ) 2 csc 2 x = 0

Got questions? Get instant answers now!

2 cos 2 x sin 2 x cos x 5 = 0

There are no solutions.

Got questions? Get instant answers now!

1 sec 2 x + 2 + sin 2 x + 4 cos 2 x = 4

Got questions? Get instant answers now!

Real-world applications

An airplane has only enough gas to fly to a city 200 miles northeast of its current location. If the pilot knows that the city is 25 miles north, how many degrees north of east should the airplane fly?

7.2

Got questions? Get instant answers now!

If a loading ramp is placed next to a truck, at a height of 4 feet, and the ramp is 15 feet long, what angle does the ramp make with the ground?

Got questions? Get instant answers now!

If a loading ramp is placed next to a truck, at a height of 2 feet, and the ramp is 20 feet long, what angle does the ramp make with the ground?

5.7

Got questions? Get instant answers now!

A woman is watching a launched rocket currently 11 miles in altitude. If she is standing 4 miles from the launch pad, at what angle is she looking up from horizontal?

Got questions? Get instant answers now!

An astronaut is in a launched rocket currently 15 miles in altitude. If a man is standing 2 miles from the launch pad, at what angle is she looking down at him from horizontal? (Hint: this is called the angle of depression.)

82.4

Got questions? Get instant answers now!

A woman is standing 8 meters away from a 10-meter tall building. At what angle is she looking to the top of the building?

Got questions? Get instant answers now!

A man is standing 10 meters away from a 6-meter tall building. Someone at the top of the building is looking down at him. At what angle is the person looking at him?

31.0

Got questions? Get instant answers now!

A 20-foot tall building has a shadow that is 55 feet long. What is the angle of elevation of the sun?

Got questions? Get instant answers now!

A 90-foot tall building has a shadow that is 2 feet long. What is the angle of elevation of the sun?

88.7

Got questions? Get instant answers now!

A spotlight on the ground 3 meters from a 2-meter tall man casts a 6 meter shadow on a wall 6 meters from the man. At what angle is the light?

Got questions? Get instant answers now!

A spotlight on the ground 3 feet from a 5-foot tall woman casts a 15-foot tall shadow on a wall 6 feet from the woman. At what angle is the light?

59.0

Got questions? Get instant answers now!

For the following exercises, find a solution to the following word problem algebraically. Then use a calculator to verify the result. Round the answer to the nearest tenth of a degree.

A person does a handstand with his feet touching a wall and his hands 1.5 feet away from the wall. If the person is 6 feet tall, what angle do his feet make with the wall?

Got questions? Get instant answers now!

A person does a handstand with her feet touching a wall and her hands 3 feet away from the wall. If the person is 5 feet tall, what angle do her feet make with the wall?

36.9

Got questions? Get instant answers now!

A 23-foot ladder is positioned next to a house. If the ladder slips at 7 feet from the house when there is not enough traction, what angle should the ladder make with the ground to avoid slipping?

Got questions? Get instant answers now!

Chapter review exercises

Solving Trigonometric Equations with Identities

For the following exercises, find all solutions exactly that exist on the interval [ 0 , 2 π ) .

Questions & Answers

x exposant 4 + 4 x exposant 3 + 8 exposant 2 + 4 x + 1 = 0
HERVE Reply
x exposent4+4x exposent3+8x exposent2+4x+1=0
HERVE
How can I solve for a domain and a codomains in a given function?
Oliver Reply
ranges
EDWIN
Thank you I mean range sir.
Oliver
proof for set theory
Kwesi Reply
don't you know?
Inkoom
find to nearest one decimal place of centimeter the length of an arc of circle of radius length 12.5cm and subtending of centeral angle 1.6rad
Martina Reply
factoring polynomial
Noven Reply
what's your topic about?
Shin Reply
find general solution of the Tanx=-1/root3,secx=2/root3
Nani Reply
find general solution of the following equation
Nani
the value of 2 sin square 60 Cos 60
Sanjay Reply
0.75
Lynne
0.75
Inkoom
when can I use sin, cos tan in a giving question
duru Reply
depending on the question
Nicholas
I am a carpenter and I have to cut and assemble a conventional roof line for a new home. The dimensions are: width 30'6" length 40'6". I want a 6 and 12 pitch. The roof is a full hip construction. Give me the L,W and height of rafters for the hip, hip jacks also the length of common jacks.
John
I want to learn the calculations
Koru Reply
where can I get indices
Kojo Reply
I need matrices
Nasasira
hi
Raihany
Hi
Solomon
need help
Raihany
maybe provide us videos
Nasasira
about complex fraction
Raihany
Hello
Cromwell
a
Amie
What do you mean by a
Cromwell
nothing. I accidentally press it
Amie
you guys know any app with matrices?
Khay
Ok
Cromwell
Solve the x? x=18+(24-3)=72
Leizel Reply
x-39=72 x=111
Suraj
Solve the formula for the indicated variable P=b+4a+2c, for b
Deadra Reply
Need help with this question please
Deadra
b=-4ac-2c+P
Denisse
b=p-4a-2c
Suddhen
b= p - 4a - 2c
Snr
p=2(2a+C)+b
Suraj
b=p-2(2a+c)
Tapiwa
P=4a+b+2C
COLEMAN
b=P-4a-2c
COLEMAN
like Deadra, show me the step by step order of operation to alive for b
John
A laser rangefinder is locked on a comet approaching Earth. The distance g(x), in kilometers, of the comet after x days, for x in the interval 0 to 30 days, is given by g(x)=250,000csc(π30x). Graph g(x) on the interval [0, 35]. Evaluate g(5)  and interpret the information. What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond? Find and discuss the meaning of any vertical asymptotes.
Kaitlyn Reply
The sequence is {1,-1,1-1.....} has
amit Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask