Trigonometric Functions and Ratios

The video tutorial covers the basics of trigonometric functions, emphasizing the necessity of triangles for evaluation. It explains the concept of reference angles and the use of the coordinate system. The tutorial demonstrates how to calculate trigonometric ratios using the Pythagorean theorem and discusses simplifying radicals and rationalizing denominators.

Why is a triangle necessary for evaluating trigonometric functions?

• Because it is the only shape with angles.

• Because it helps in understanding the unit circle.

• Because it is a basic geometric shape.

• Because it simplifies calculations.

What is a reference angle?

• An angle that is always obtuse.

• An acute angle between the terminal side and the x-axis.

• An angle that is equal to 90 degrees.

• An angle that is always negative.

How do you create a right triangle using a reference angle?

• By drawing a perpendicular line to the x-axis.

• By drawing a parallel line to the y-axis.

• By drawing a diagonal line across the coordinate plane.

• By drawing a circle around the angle.

What is the purpose of using a coordinate system in trigonometry?

• To determine the side lengths of triangles.

• To simplify the unit circle.

• To make calculations more complex.

• To avoid using the Pythagorean theorem.

How do you find the hypotenuse of a triangle using the Pythagorean theorem?

• By dividing the squares of the two sides.

• By subtracting the squares of the two sides.

• By adding the squares of the two sides and taking the square root.

• By multiplying the two sides and taking the square root.

What is the sine of an angle in a right triangle?

• The ratio of the hypotenuse to the opposite side.

• The ratio of the opposite side to the adjacent side.

• The ratio of the opposite side to the hypotenuse.

• The ratio of the adjacent side to the hypotenuse.

What is the cosine of an angle in a right triangle?

• The ratio of the adjacent side to the hypotenuse.

• The ratio of the opposite side to the hypotenuse.

• The ratio of the hypotenuse to the adjacent side.

• The ratio of the opposite side to the adjacent side.

What is the tangent of an angle in a right triangle?

• The ratio of the hypotenuse to the opposite side.

• The ratio of the adjacent side to the hypotenuse.

• The ratio of the opposite side to the adjacent side.

• The ratio of the hypotenuse to the adjacent side.

How do you find the cosecant of an angle?

• By taking the reciprocal of the hypotenuse.

• By taking the reciprocal of the sine.

• By taking the reciprocal of the cosine.

• By taking the reciprocal of the tangent.

Why is it important to rationalize the denominator in trigonometric ratios?

• To make the expression more complex.

• To simplify the expression.

• To avoid using the Pythagorean theorem.

• To change the value of the expression.