Pythagorean Identities and Trigonometric Functions

The video tutorial by Mr. Banker covers the three basic Pythagorean identities in trigonometry: sine squared plus cosine squared equals one, secant squared equals one plus tangent squared, and cosecant squared equals one plus cotangent squared. The tutorial explains how to rearrange these identities to derive other forms and applies them to solve problems, such as finding sine and cosine values given a tangent value.

What is the first Pythagorean identity introduced in the video?

• tangent squared of theta equals secant squared of theta minus one

• cosecant squared of theta equals one plus cotangent squared of theta

• secant squared of theta equals one plus tangent squared of theta

• sine squared of theta plus cosine squared of theta equals one

How can the first Pythagorean identity be rearranged to express sine squared of theta?

• sine squared of theta equals cosine squared of theta minus one

• sine squared of theta equals one plus cosine squared of theta

• sine squared of theta equals one minus cosine squared of theta

• sine squared of theta equals one over cosine squared of theta

What is the second Pythagorean identity introduced in the video?

• sine squared of theta plus cosine squared of theta equals one

• cosecant squared of theta equals one plus cotangent squared of theta

• tangent squared of theta equals secant squared of theta minus one

• secant squared of theta equals one plus tangent squared of theta

How can the second Pythagorean identity be rearranged to express tangent squared of theta?

• tangent squared of theta equals one over secant squared of theta

• tangent squared of theta equals secant squared of theta minus one

• tangent squared of theta equals secant squared of theta plus one

• tangent squared of theta equals one minus secant squared of theta

What is the third Pythagorean identity introduced in the video?

• cosecant squared of theta equals one plus cotangent squared of theta

• sine squared of theta plus cosine squared of theta equals one

• secant squared of theta equals one plus tangent squared of theta

• tangent squared of theta equals secant squared of theta minus one

How can the third Pythagorean identity be rearranged to express cotangent squared of theta?

• cotangent squared of theta equals one over cosecant squared of theta

• cotangent squared of theta equals cosecant squared of theta minus one

• cotangent squared of theta equals cosecant squared of theta plus one

• cotangent squared of theta equals one minus cosecant squared of theta

Given that the tangent of theta is 5, what is the secant squared of theta?

• 26

• 1

• 25

• 5

If the secant of theta is plus or minus the square root of 26, what is the cosine of theta?

• 1 over 26

• 26

• 1 over the square root of 26

• square root of 26

How can the sine of theta be found if the tangent of theta is 5 and the cosine of theta is 1 over the square root of 26?

• Multiply the tangent of theta by the cosine of theta

• Divide the tangent of theta by the cosine of theta

• Add the tangent of theta to the cosine of theta

• Subtract the tangent of theta from the cosine of theta

What is the sine of theta if the tangent of theta is 5 and the cosine of theta is 1 over the square root of 26?

• 5 minus the square root of 26

• 5 plus the square root of 26

• 5 over the square root of 26

• 5 times the square root of 26