Understanding Pythagorean Identities

The video tutorial explains the three Pythagorean identities in trigonometry and demonstrates how to use them to calculate unknown trigonometric values. It provides three examples: finding cosine when sine is known, finding sine when cosine is known, and determining cosine with given sine and tangent conditions. The tutorial emphasizes the importance of understanding quadrants to determine the sign of trigonometric values.

Which of the following is a Pythagorean identity?

• sine squared theta plus cosine squared theta equals one

• tangent squared theta equals secant squared theta

• sine theta plus cosine theta equals one

• cotangent squared theta equals cosecant squared theta

If sine theta is 4/5 and theta is in the first quadrant, what is cosine theta?

• -4/5

• 4/5

• -3/5

• 3/5

In the first quadrant, which trigonometric function is always positive?

• All of the above

• Tangent

• Cosine

• Sine

If cosine theta is 8/17 and theta is in the fourth quadrant, what is sine theta?

• -8/17

• 8/17

• -15/17

• 15/17

In which quadrant is sine negative and cosine positive?

• First

• Fourth

• Second

• Third

If sine theta is 2/5 and tangent theta is negative, what is cosine theta?

• 2/5

• sqrt(21)/5

• -2/5

• -sqrt(21)/5

In which quadrants is tangent negative?

• First and Second

• First and Third

• Second and Fourth

• Third and Fourth

Which quadrant has both sine and tangent positive?

• Fourth

• Third

• Second

• First

What is the value of cosine theta if sine theta is 2/5 and theta is in the fourth quadrant?

• sqrt(21)/5

• -sqrt(21)/5

• 2/5

• -2/5

Which identity is used to find cosine when sine is known?

• sine theta plus cosine theta equals one

• sine squared theta plus cosine squared theta equals one

• tangent squared theta plus one equals secant squared theta

• cotangent squared theta plus one equals cosecant squared theta