Finding Exact Values of Trigonometric Functions in the Unit Circle

The video tutorial covers trigonometric ratios—sine, cosine, and tangent—using the unit circle. It explains how these ratios relate to the coordinate plane and provides examples of calculating these ratios for various angles in both radians and degrees. The tutorial emphasizes understanding reference angles and quadrant positions to determine the sign and value of trigonometric functions.

What does the sine of an angle in the unit circle represent?

• The hypotenuse of the triangle

• The ratio of the opposite side to the adjacent side

• The y-coordinate of the point

• The x-coordinate of the point

In the unit circle, what is the value of the hypotenuse for any triangle formed?

• Equal to the radius of the circle

• Always 0

• Always 2

• Dependent on the angle

How is cosine represented in the unit circle?

• As the y-coordinate

• As the ratio of adjacent over opposite

• None of the above

• As the x-coordinate

What is the tangent of an angle in the unit circle defined as?

• Opposite over hypotenuse

• Adjacent over hypotenuse

• X-coordinate over y-coordinate

• Y-coordinate over x-coordinate

If an angle is in the third quadrant, what are the signs of the sine and cosine values?

• Sine positive, cosine negative

• Both sine and cosine are negative

• Sine negative, cosine positive

• Both sine and cosine are positive

What is the reference angle for an angle measurement of 5 PI over 4 in radians?

• 60 degrees

• 90 degrees

• 30 degrees

• 45 degrees

How do you find the cosine of an angle in the unit circle?

• It is the x-coordinate of the point

• It is the y-coordinate of the point

• It is the ratio of the opposite side to the adjacent side

• It is the hypotenuse of the triangle

What is the sine of 4 PI over 3 in the unit circle?

• 1/2

• -1/2

• -Square root of 3 over 2

• Square root of 3 over 2

Which quadrant does an angle of 210 degrees fall into?

• Fourth quadrant

• Third quadrant

• Second quadrant

• First quadrant

What is the tangent of an angle if both the opposite and adjacent sides are negative?

• Negative

• Positive

• Zero

• Undefined