Trigonometric Functions and Relationships

This video tutorial explains how to evaluate the six trigonometric functions when given limited information, such as the sine of an angle and its quadrant. The instructor uses the unit circle and right triangle to determine side lengths and hypotenuse, applying the Pythagorean theorem. The video covers calculating sine, cosine, tangent, and their reciprocal functions, emphasizing the importance of understanding the unit circle and right triangle in trigonometry.

What are the two main tools used to evaluate trigonometric functions when given limited information?

• Unit circle and Pythagorean theorem

• Cosine rule and unit circle

• Unit circle and right triangle

• Right triangle and sine rule

In which quadrant is angle T located if S(T) is negative and T is given as in quadrant three?

• Quadrant 2

• Quadrant 3

• Quadrant 1

• Quadrant 4

What is the relationship between the sides of a right triangle used to find the hypotenuse?

• A^2 + B^2 = 2C^2

• A^2 = B^2 + C^2

• A^2 + B^2 = C^2

• A^2 - B^2 = C^2

If the sine of angle T is -3/5, what is the cosecant of T?

• -5/3

• 3/5

• -3/5

• 5/3

What is the cosine of angle T if the adjacent side is -4 and the hypotenuse is 5?

• 5/4

• -4/5

• 4/5

• -5/4

What is the secant of angle T if the cosine is -4/5?

• 5/4

• -4/5

• 4/5

• -5/4

How is the tangent of angle T defined in a right triangle?

• Adjacent side over hypotenuse

• Hypotenuse over opposite side

• Opposite side over hypotenuse

• Opposite side over adjacent side

What is the cotangent of angle T if the tangent is 3/4?

• 4/3

• 3/4

• -4/3

• -3/4

Why is it important to draw a unit circle when evaluating trigonometric functions?

• To determine the length of the hypotenuse

• To identify the quadrant and signs of coordinates

• To calculate the area of the triangle

• To find the exact angle measure

What should you do if you only know the value of sine or cosine?

• Use the sine rule to find the angle

• Use the cosine rule to find the angle

• Find the third side using the Pythagorean theorem

• Estimate the angle using a calculator