<< 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 ) .

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




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