Trigonometric Functions and Properties

The video tutorial explains the relationship between the sine and cosine of complementary angles using a right triangle. It introduces the concept with the cosine of 58 degrees and the sine of 32 degrees, demonstrating how these values are equal due to their complementary nature. The tutorial uses the SOHCAHTOA definitions to explain the trigonometric ratios and generalizes the concept for any angle, emphasizing the property that the sine of an angle equals the cosine of its complement.

What is the cosine of 58 degrees approximately equal to?

• 0.32

• 0.75

• 0.58

• 0.53

In a right triangle, what is the sum of the two non-right angles?

• 32 degrees

• 180 degrees

• 58 degrees

• 90 degrees

What does the acronym SOHCAHTOA help you remember?

• The relationships between angles and side lengths in a triangle

• The sum of angles in a triangle

• The types of triangles

• The area of a triangle

Which side is opposite the 32-degree angle in the given triangle?

• BC

• AB

• None

• AC

What is the sine of 32 degrees equal to in terms of cosine?

• Cosine of 58 degrees

• Sine of 90 degrees

• Cosine of 32 degrees

• Sine of 58 degrees

What is the general property of sine and cosine for complementary angles?

• Cosine of an angle equals cosine of its complement

• Sine of an angle equals sine of its complement

• Sine of an angle equals tangent of its complement

• Sine of an angle equals cosine of its complement

If the sine of an angle is 0.5, what is the cosine of its complement?

• 0.5

• 0.7

• 0.6

• 0.8

What is the complement of a 25-degree angle?

• 75 degrees

• 65 degrees

• 55 degrees

• 85 degrees

If the cosine of an angle is 0.8, what is the sine of its complement?

• 0.8

• 0.2

• 0.6

• 0.4

What is the sine of 90 degrees minus theta equal to?

• Sine of theta

• Secant of theta

• Cosine of theta

• Tangent of theta