Trigonometric Functions and Right Triangles

This video tutorial explains how to evaluate the six trigonometric functions when given limited information, such as a specific trigonometric value and the quadrant of an angle. The instructor demonstrates using the unit circle and right triangle to solve these problems, emphasizing the importance of the Pythagorean theorem for calculating side lengths. The video covers the evaluation of sine, cosine, tangent, and their reciprocal functions, providing a comprehensive understanding of trigonometric function evaluation.

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

• Cosine rule and unit circle

• Right triangle and sine rule

• Unit circle and right triangle

• Unit circle and Pythagorean theorem

In which quadrant is angle T located if S(T) is negative and T is in quadrant 3?

• Quadrant 1

• Quadrant 2

• Quadrant 3

• Quadrant 4

What is the importance of drawing a right triangle back to the x-axis?

• To create a right angle

• To align with the y-axis

• To ensure the triangle is isosceles

• To make the triangle equilateral

How do you find the length of the missing side in a right triangle using the Pythagorean theorem?

• Multiply the two known sides

• Add the squares of the two sides and take the square root

• Subtract the square of one side from the hypotenuse

• Add the squares of the two known sides

What is the reciprocal of the sine function?

• Cosecant

• Secant

• Cosine

• Tangent

If the cosine of angle T is -4/5, what is the secant of T?

• -5/4

• -4/5

• 4/5

• 5/4

What is the tangent of angle T if the opposite side is -3 and the adjacent side is 4?

• 3/4

• -4/3

• -3/4

• 4/3

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

• 4/3

• -4/3

• 3/4

• -3/4

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

• To determine the size of the angle

• To find the radius of the circle

• To identify the quadrant and sign of coordinates

• To calculate the area of the circle

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

• Use the cosine rule

• Use the sine rule

• Find the third side using the Pythagorean theorem

• Calculate the area of the triangle