Trigonometric Equations and Solutions

The video tutorial covers solving trigonometric equations involving sine, tangent, cosine, and secant functions. It explains how to isolate the trigonometric function, use the unit circle to find reference angles, and write general solutions. The tutorial also discusses solving equations within a restricted domain and provides examples for each type of trigonometric function.

What is the first step in solving the equation sine of 2x equals 1?

• Subtract 1 from both sides

• Add 1 to both sides

• Divide both sides by 2

• Multiply both sides by 2

On the unit circle, where does the sine value equal 1/2?

• At 45 degrees

• At 90 degrees

• At 60 degrees

• At 30 degrees

What is the general solution for 2x when sine of 2x equals 1/2?

• 2x = PI/3 + 2PI n

• 2x = PI/6 + 2PI n

• 2x = PI/4 + 2PI n

• 2x = PI/2 + 2PI n

How do you solve for x from the general solution of 2x?

• Multiply by 2

• Add PI

• Divide by 2

• Subtract PI

What is the first step in solving the equation 3 tangent squared of 4x minus 1 equals 0?

• Divide by 3

• Add 1 to both sides

• Multiply by 3

• Subtract 1 from both sides

Where does tangent equal square root of 3 over 3 on the unit circle?

• At 90 degrees

• At 45 degrees

• At 60 degrees

• At 30 degrees

What is the general solution for 4x when tangent of 4x equals square root of 3 over 3?

• 4x = PI/4 + PI n

• 4x = PI/2 + PI n

• 4x = PI/6 + PI n

• 4x = PI/3 + PI n

What is the first step in solving the equation 2 times the cosine of x divided by 2 equals square root of 3?

• Add square root of 3 to both sides

• Divide both sides by 2

• Multiply both sides by 2

• Subtract square root of 3 from both sides

Where does cosine equal square root of 3 over 2 on the unit circle?

• At 90 degrees

• At 45 degrees

• At 60 degrees

• At 30 degrees

What is the general solution for x/2 when cosine of x/2 equals square root of 3 over 2?

• x/2 = 90 degrees + 360 n

• x/2 = 45 degrees + 360 n

• x/2 = 30 degrees + 360 n

• x/2 = 60 degrees + 360 n