Trigonometric Functions and Their Values

The video tutorial covers the basics of right triangles and trigonometric functions, including sine, cosine, and tangent. It explains how these functions relate to the sides of a triangle and their behavior in different quadrants. The tutorial also provides examples of calculating trigonometric functions for specific points, demonstrating the process of plotting points, forming triangles, and using the Pythagorean theorem to find the hypotenuse. The mnemonic 'All Students Take Calculus' is introduced to help remember the signs of trigonometric functions in each quadrant.

What is the reciprocal of the sine function?

• Secant

• Cosecant

• Tangent

• Cotangent

In which quadrants is the cosine function positive?

• Quadrants I and IV

• Quadrants II and III

• Quadrants I and II

• Quadrants III and IV

According to the mnemonic 'All Students Take Calculus', which function is positive in the third quadrant?

• Cosine

• Cosecant

• Sine

• Tangent

Given the point (-5, 12), what is the value of sine theta?

• -12/13

• -5/13

• 12/13

• 5/13

For the point (-5, 12), what is the value of cotangent theta?

• -5/12

• 5/12

• 12/5

• -12/5

In the example with point (-8, -15), which trigonometric function is positive?

• Tangent

• Cosine

• Secant

• Sine

For the point (-8, -15), what is the value of secant theta?

• -17/8

• 8/17

• 17/8

• -8/17

Using the point (2, -4), what is the hypotenuse length calculated using the Pythagorean theorem?

• 5

• 4√5

• √20

• 2√5

For the point (2, -4), what is the value of cosine theta after rationalizing the denominator?

• 2/√5

• √5/5

• 1/√5

• 5/√5

In the example with point (2, -4), what is the value of cotangent theta?

• -1/2

• 1/2

• 2

• -2