Basic Trigonometric Identities: Pythagorean Identities and Cofunction Identities

The video tutorial covers trigonometric identities, starting with an introduction to the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. It explains the reciprocal relationships among these functions and delves into specific identities, such as tangent being sine over cosine and cotangent being cosine over sine. The Pythagorean identities are derived using the Pythagorean theorem, leading to expressions like sine squared plus cosine squared equals one. The tutorial also explores cofunction identities, showing how sine and cosine relate to complementary angles using the unit circle.

Which of the following is a reciprocal pair of trigonometric functions?

• Sine and Secant

• Tangent and Cotangent

• Cosine and Secant

• Sine and Tangent

What is the Pythagorean identity for sine and cosine?

• sine squared theta minus cosine squared theta equals 1

• sine theta times cosine theta equals 1

• sine theta plus cosine theta equals 1

• sine squared theta plus cosine squared theta equals 1

If you divide the Pythagorean identity by cosine squared theta, what identity do you get?

• tangent squared plus 1 equals cosecant squared

• 1 plus tangent squared equals secant squared

• 1 plus cotangent squared equals cosecant squared

• sine squared plus cosine squared equals 1

What is the relationship between sine and cosine for complementary angles?

• Sine of theta equals cosine of 90 minus theta

• Cosine of theta equals cosine of 90 minus theta

• Sine of theta equals sine of 90 minus theta

• Cosine of theta equals sine of theta

Which identity is true for complementary angles?

• Tangent of theta equals cotangent of 90 minus theta

• Sine of theta equals tangent of 90 minus theta

• Secant of theta equals cosecant of 90 minus theta

• Cosine of theta equals secant of 90 minus theta