Trigonometric Functions and Unit Circle

This video tutorial covers solving common questions related to the unit circle. It begins with finding missing coordinates using the unit circle equation, followed by verifying points on the circle and using symmetry to find additional points. The tutorial concludes with calculating six trigonometric functions for a given point on the unit circle, using the Pythagorean theorem to find the hypotenuse and applying trigonometric identities.

What is the formula used to find the missing coordinate on the unit circle?

• x^2 + y^2 = 1

• x^2 - y^2 = 1

• x + y = 1

• x - y = 1

If the x-coordinate of a point on the unit circle is -1/8, what are the possible values for the y-coordinate?

• Neither

• Both positive and negative

• Only negative

• Only positive

How can you verify that a point lies on the unit circle?

• By checking if x + y equals 1

• By checking if x^2 + y^2 equals 1

• By checking if x^2 - y^2 equals 1

• By checking if x - y equals 1

What is the role of symmetry in finding points on the unit circle?

• It helps find four additional points

• It helps find three additional points

• It helps find two additional points

• It helps find one additional point

Which of the following is NOT a trigonometric function?

• Secant

• Sine

• Cosine

• Tangent

What is the reciprocal of the sine function?

• Secant

• Cosecant

• Cotangent

• Tangent

If the opposite side of a triangle is the square root of 15 over 4, what is the sine of the angle?

• 15 over 2

• 15 over 4

• Square root of 15 over 2

• Square root of 15 over 4

What is the cosine of an angle if the adjacent side is -0.25?

• -1/4

• 1/4

• -1/2

• 1/2

How do you find the cotangent of an angle?

• Reciprocal of sine

• Reciprocal of cosine

• Reciprocal of tangent

• Reciprocal of secant

What is the value of secant if the cosine is -1/4?

• -4

• 4

• 1/4

• -1/4