Understanding Circle Coordinates and Trigonometry

The video tutorial explains how to find the coordinates of a point on a circle with a radius of 12, corresponding to an angle of 50 degrees. It involves constructing a reference triangle and using trigonometric functions, specifically sine and cosine, to calculate the x and y coordinates. The tutorial emphasizes the importance of ensuring the calculator is in degree mode and demonstrates how to round the results to three decimal places. The final coordinates are presented as an ordered pair.

What is the radius of the circle mentioned in the video?

• 12

• 10

• 20

• 15

What angle is used to find the coordinates on the circle?

• 30 degrees

• 60 degrees

• 50 degrees

• 45 degrees

In forming the reference triangle, which side is labeled as the opposite side?

• X

• Y

• Hypotenuse

• Radius

What is the relationship between cosine and the sides of the triangle?

• Cosine is the ratio of hypotenuse to opposite

• Cosine is the ratio of adjacent to hypotenuse

• Cosine is the ratio of hypotenuse to adjacent

• Cosine is the ratio of opposite to hypotenuse

How do you express X in terms of cosine and the radius?

• X = 12 * cosine 50 degrees

• X = 12 + cosine 50 degrees

• X = 12 / cosine 50 degrees

• X = 12 - cosine 50 degrees

What formula is used to find Y in terms of sine and the radius?

• Y = 12 - sine 50 degrees

• Y = 12 * sine 50 degrees

• Y = 12 + sine 50 degrees

• Y = 12 / sine 50 degrees

What is the approximate value of the X-coordinate after calculation?

• 10.000

• 9.193

• 7.713

• 8.000

What is the approximate value of the Y-coordinate after calculation?

• 9.193

• 10.000

• 7.713

• 8.000

What mode should the calculator be in to ensure correct trigonometric calculations?

• Standard mode

• Scientific mode

• Degree mode

• Radian mode

What is the ordered pair representing the point on the circle?

• (9.193, 7.713)

• (7.713, 9.193)

• (8.000, 9.193)

• (7.713, 8.000)