9.5 Solving trigonometric equations  (Page 8/10)

$6{\tan }^{2}x+13\tan x=\mathrm{-6}$

${\tan }^{2}x-\sec x=1$

${\sin }^{2}x-2{\cos }^{2}x=0$

$2{\tan }^{2}x+9\tan x-6=0$

$4{\sin }^{2}x+\sin \left(2x\right)\sec x-3=0$

${\csc }^{2}x-3\csc x-4=0$

${\sin }^{2}x-{\cos }^{2}x-1=0$

${\sin }^{2}x\left(1-{\sin }^{2}x\right)+{\cos }^{2}x\left(1-{\sin }^{2}x\right)=0$

$3{\sec }^{2}x+2+{\sin }^{2}x-{\tan }^{2}x+{\cos }^{2}x=0$

${\sin }^{2}x-1+2\cos \left(2x\right)-{\cos }^{2}x=1$

${\tan }^{2}x-1-{\sec }^{3}x\cos x=0$

$\frac{\sin \left(2x\right)}{{\sec }^{2}x}=0$

$\frac{\sin \left(2x\right)}{2{\csc }^{2}x}=0$

$2{\cos }^{2}x-{\sin }^{2}x-\cos x-5=0$

$\frac{1}{{\sec }^{2}x}+2+{\sin }^{2}x+4{\cos }^{2}x=4$

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?

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?

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?

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?

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.)

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?

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?

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

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

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?

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?

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?

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?

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?