Trigonometric Functions and Angles

The video tutorial explains how to use reference angles to evaluate trigonometric functions for negative angles, specifically negative 405 degrees. It covers determining the quadrant of the angle, using coterminal angles to find a positive equivalent, and calculating the reference angle. The tutorial concludes with evaluating sine, cosine, and tangent using the reference angle, emphasizing the importance of quadrant signs.

What is the primary purpose of using reference angles?

• To simplify the calculation of trigonometric functions for any angle.

• To convert angles from degrees to radians.

• To find the exact value of angles in the first quadrant.

• To determine the length of the hypotenuse in a right triangle.

How can you determine the quadrant of a negative angle?

• By converting it to radians.

• By sketching it on the unit circle.

• By using a calculator.

• By adding 90 degrees to it.

Why is it important to know the quadrant of an angle?

• To convert the angle to radians.

• To know the sign of the trigonometric functions.

• To find the angle's reference angle.

• To determine the angle's exact value.

What is a coterminal angle?

• An angle that is always negative.

• An angle that is exactly 90 degrees.

• An angle that shares the same initial and terminal sides.

• An angle that is always positive.

How do you find a positive coterminal angle for a negative angle?

• By adding 360 degrees.

• By adding 180 degrees.

• By subtracting 360 degrees.

• By multiplying by -1.

What is the reference angle for 315 degrees in the fourth quadrant?

• 30 degrees

• 45 degrees

• 90 degrees

• 60 degrees

How do you calculate the reference angle in the fourth quadrant?

• Theta prime = 180 - theta

• Theta prime = theta + 360

• Theta prime = 360 - theta

• Theta prime = theta - 180

What is the sine of a 45-degree angle in the fourth quadrant?

• Square root of 2 over 2

• -Square root of 2 over 2

• 1

• -1

What is the cosine of a 45-degree angle in the fourth quadrant?

• Square root of 2 over 2

• 0

• 1

• -Square root of 2 over 2

What is the tangent of a 45-degree angle in the fourth quadrant?

• -1

• Square root of 2

• 1

• 0