Trigonometric Identities and Functions

This video tutorial covers the proof of trigonometric identities using the Pythagorean theorem. It begins with a review of trigonometric ratios, including sine, cosine, and tangent. The video then explains the Pythagorean theorem and demonstrates how it is used to prove three key trigonometric identities: sine squared plus cosine squared equals one, one plus tangent squared equals secant squared, and one plus cotangent squared equals cosecant squared. The tutorial concludes with additional tips and a reminder of the relationships between trigonometric functions.

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

• Adjacent over hypotenuse

• Opposite over hypotenuse

• Adjacent over opposite

• Hypotenuse over opposite

Which trigonometric ratio is defined as opposite over adjacent?

• Sine

• Secant

• Cosine

• Tangent

According to the Pythagorean theorem, what is the relationship between the sides of a right triangle?

• The sum of the squares of the hypotenuse and one leg is equal to the square of the other leg

• The sum of the squares of the two legs is equal to the square of the hypotenuse

• The product of the two legs is equal to the hypotenuse

• The difference of the squares of the two legs is equal to the square of the hypotenuse

Which of the following is NOT a trigonometric identity introduced in the video?

• One plus tangent squared theta equals secant squared theta

• Sine squared theta plus cosine squared theta equals one

• Sine theta plus cosine theta equals one

• One plus cotangent squared theta equals cosecant squared theta

What is the first step in proving the identity sine squared theta plus cosine squared theta equals one?

• Add sine squared theta to both sides

• Divide the equation by the hypotenuse squared

• Subtract cosine squared theta from both sides

• Multiply the equation by the hypotenuse

In the proof of the identity 1 + tan^2(theta) = sec^2(theta), what is tan(theta) expressed as?

• Opposite over hypotenuse

• Hypotenuse over adjacent

• Adjacent over hypotenuse

• Opposite over adjacent

What is the reciprocal of cosine theta?

• Cosecant theta

• Secant theta

• Sine theta

• Tangent theta

Which identity is proven by dividing the Pythagorean theorem by the opposite side squared?

• Sine theta equals cosine theta

• One plus cotangent squared theta equals cosecant squared theta

• One plus tangent squared theta equals secant squared theta

• Sine squared theta plus cosine squared theta equals one

What is the reciprocal of tangent theta?

• Cosecant theta

• Cotangent theta

• Secant theta

• Sine theta

If sine theta is 1/2, what is cosine theta when theta is between 0 and 90 degrees?

• 1/2

• Root 3 over 2

• 1

• Root 2 over 2