Trigonometric Functions and Ratios

The video tutorial introduces the six trigonometric ratios derived from a right triangle: sine, cosine, tangent, cotangent, secant, and cosecant. It explains the relationships between the sides of a right triangle and these ratios, using the mnemonic 'SOHCAHTOA' for easy memorization. The tutorial also covers the reciprocal nature of cotangent, secant, and cosecant. Examples are provided to demonstrate how to calculate angles and side lengths using these ratios, emphasizing the use of a scientific calculator for accuracy.

In a right triangle, what is the side opposite the right angle called?

• Hypotenuse

• Adjacent

• Base

• Opposite

What is the formula for sine in a right triangle?

• Opposite over Adjacent

• Opposite over Hypotenuse

• Hypotenuse over Opposite

• Adjacent over Hypotenuse

Which mnemonic helps remember the primary trigonometric ratios?

• Cosine Rule

• Sine Rule

• Pythagorean

• SOHCAHTOA

What is the reciprocal of the tangent function?

• Cotangent

• Cosecant

• Cosine

• Secant

How is secant related to cosine?

• Secant is the square of cosine

• Secant is the reciprocal of cosine

• Secant is the same as cosine

• Secant is the inverse of cosine

If the opposite side is 3 and the hypotenuse is 5, what is sine theta?

• 3/4

• 5/3

• 4/5

• 3/5

Given a triangle with sides 3, 4, and 5, what is the value of cosine theta?

• 3/5

• 4/5

• 5/4

• 3/4

To find an angle using sine, which calculator function is used?

• sin

• sin⁻¹

• cos

• tan

If angle theta is 36 degrees and side b is 8.4, which function helps find side a?

• Sine

• Cosine

• Tangent

• Cosecant

What is the length of the hypotenuse if side b is 8.4 and angle theta is 36 degrees?

• 6.1

• 8.4

• 10.38

• 9.2