Trigonometric Angles and Quadrants

The video tutorial explains how to find an angle theta between 0 and 360 degrees such that sine 40 degrees equals sine theta. It begins by sketching the reference triangle for 40 degrees and analyzing the coordinates in the first quadrant. The tutorial then explores finding an angle with the same sine value in the second quadrant and an angle with the same cosine value in the fourth quadrant. The video concludes with tips on modeling reference triangles on the coordinate plane.

What is the range of angle theta that we are trying to find?

• 0 to 270 degrees

• 0 to 90 degrees

• 0 to 360 degrees

• 0 to 180 degrees

In which quadrant are both the x and y coordinates positive?

• Third quadrant

• Fourth quadrant

• Second quadrant

• First quadrant

What is the reference angle for the angle in the second quadrant that has the same sine value as 40 degrees?

• 40 degrees

• 50 degrees

• 90 degrees

• 140 degrees

What is the angle in the second quadrant that has the same sine value as 40 degrees?

• 140 degrees

• 130 degrees

• 150 degrees

• 90 degrees

What is the formula for cosine theta in terms of x and r?

• x divided by y

• r divided by x

• x divided by r

• y divided by r

In which quadrant is the x-coordinate positive and the y-coordinate negative?

• Fourth quadrant

• Third quadrant

• Second quadrant

• First quadrant

What is the reference angle for the angle in the fourth quadrant that has the same cosine value as 40 degrees?

• 90 degrees

• 40 degrees

• 320 degrees

• 50 degrees

What is the angle in the fourth quadrant that has the same cosine value as 40 degrees?

• 320 degrees

• 270 degrees

• 330 degrees

• 310 degrees

Why does the y-coordinate not matter when finding the cosine value?

• Because y-coordinate is always negative

• Because y-coordinate is always positive

• Because cosine is only concerned with the y-coordinate

• Because cosine is only concerned with the x-coordinate

What is the importance of modeling reference triangles on the coordinate plane?

• To find the exact angle

• To determine the quadrant

• To visualize the angle and its coordinates

• To calculate the hypotenuse