Trigonometric Functions and Ratios

This video tutorial explains how to find the exact trigonometric function values using a right triangle. It begins with identifying the need for all three side lengths and uses the Pythagorean theorem to calculate the hypotenuse. The tutorial reviews the definitions of sine, cosine, tangent, and their reciprocals, and demonstrates how to calculate these values for a specific angle. It also covers rationalizing and simplifying these values for clarity.

Why is it necessary to know the lengths of all three sides of a triangle to find all six trigonometric function values?

• To ensure the triangle is a right triangle

• To apply the Pythagorean theorem

• To calculate the ratios for each function

• To determine the angle measures

What is the first step in finding the hypotenuse of a right triangle when given the other two sides?

• Multiply the lengths of the two sides

• Use the Pythagorean theorem

• Add the lengths of the two sides

• Subtract the lengths of the two sides

What is the simplified form of the square root of 45?

• √45

• 5√3

• 3√5

• 9√5

Which trigonometric function is the reciprocal of sine?

• Tangent

• Cosecant

• Secant

• Cosine

How is the sine of an angle defined in a right triangle?

• Ratio of hypotenuse to opposite side

• Ratio of adjacent side to opposite side

• Ratio of adjacent side to hypotenuse

• Ratio of opposite side to hypotenuse

What is the rationalized form of 1/√5?

• 5/√5

• 1/5

• √5/5

• √5

What is the cosine of angle B if the adjacent side is 6 and the hypotenuse is 3√5?

• 2/√5

• 6/√5

• 1/√5

• 3/√5

What is the reciprocal of the cosine function?

• Cotangent

• Secant

• Cosecant

• Tangent

How is the tangent of an angle defined in a right triangle?

• Ratio of hypotenuse to adjacent side

• Ratio of hypotenuse to opposite side

• Ratio of adjacent side to hypotenuse

• Ratio of opposite side to adjacent side

What is the cotangent of angle B if the tangent is 1/2?

• 3

• 1

• 2

• 1/2