3.5 Solving trigonometric equations  (Page 7/7)

$2\sin \theta =\mathrm{-}\sqrt{2}$

$2\sin \theta =\sqrt{3}$

$2\cos \theta =1$

$2\cos \theta =\mathrm{-}\sqrt{2}$

$\tan \theta =\mathrm{-1}$

$\tan x=1$

$\cot x+1=0$

$4{\sin }^{2}x-2=0$

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

$2\cos \theta =\sqrt{2}$

$2\cos \theta =\mathrm{-1}$

$2\sin \theta =\mathrm{-1}$

$2\sin \theta =\mathrm{-}\sqrt{3}$

$2\sin \left(3\theta \right)=1$

$2\sin \left(2\theta \right)=\sqrt{3}$

$2\cos \left(3\theta \right)=-\sqrt{2}$

$\cos \left(2\theta \right)=-\frac{\sqrt{3}}{2}$

$2\sin \left(\pi \theta \right)=1$

$2\cos \left(\frac{\pi }{5}\theta \right)=\sqrt{3}$

$\sec (x)\sin (x)-2\sin (x)=0$

$\tan (x)-2\sin (x)\tan (x)=0$

$2{\cos }^{2}t+\cos \left(t\right)=1$

$2{\tan }^2(t)=3\sec (t)$

$2\sin (x)\cos (x)-\sin (x)+2\cos (x)-1=0$

${\cos }^2\theta =\frac{1}{2}$

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

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

$8{\sin }^2(x)+6\sin (x)+1=0$

${\tan }^5(x)=\tan (x)$

$\sin (3x)\cos (6x)-\cos (3x)\sin (6x)=\mathrm{-0.9}$

$\sin (6x)\cos (11x)-\cos (6x)\sin (11x)=\mathrm{-0.1}$

$\cos \left(2x\right)\cos x+\sin \left(2x\right)\sin x=1$

$6\sin \left(2t\right)+9\sin t=0$

$9\cos \left(2\theta \right)=9{\cos }^2\theta -4$

$\sin \left(2t\right)=\cos t$

$\cos \left(2t\right)=\sin t$

$\cos (6x)-\cos (3x)=0$

${\tan }^{2}x-\sqrt{3}\tan x=0$

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

${\sin }^{2}x-2\sin x-4=0$

$5{\cos }^{2}x+3\cos x-1=0$

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

$5{\sin }^{2}x+2\sin x-1=0$

${\tan }^{2}x+5\tan x-1=0$

${\cot }^{2}x=-\cot x$

$-{\tan }^{2}x-\tan x-2=0$

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

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

$\sin \left(2x\right)-\sin x=0$

$\cos \left(2x\right)-\cos x=0$

$\frac{2\tan x}{2-{\sec }^{2}x}-{\sin }^{2}x={\cos }^{2}x$

$1-\cos (2x)=1+\cos (2x)$

${\sec }^{2}x=7$

$10\sin x\cos x=6\cos x$

$\mathrm{-3}\sin t=15\cos t\sin t$

$4{\cos }^{2}x-4=15\cos x$

$8{\sin }^{2}x+6\sin x+1=0$

$8{\cos }^2\theta =3-2\cos \theta$

$6{\cos }^{2}x+7\sin x-8=0$

$12{\sin }^{2}t+\cos t-6=0$

$\tan x=3\sin x$

${\cos }^{3}t=\cos t$

$6{\sin }^{2}x-5\sin x+1=0$

$8{\cos }^{2}x-2\cos x-1=0$

$100{\tan }^{2}x+20\tan x-3=0$

$2{\cos }^{2}x-\cos x+15=0$

$20{\sin }^{2}x-27\sin x+7=0$

$2{\tan }^{2}x+7\tan x+6=0$

$130{\tan }^{2}x+69\tan x-130=0$

$\sin x=0.27$

$\sin x=\mathrm{-0.55}$

$\tan x=\mathrm{-0.34}$

$\cos x=0.71$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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?