Trigonometric Functions and Properties

The video tutorial explains how to find trigonometric functions using a point on the terminal side of an angle. It begins by constructing a right triangle in standard position with a given point, identifying it as a 45-45-90 triangle. The tutorial then calculates the sine, cosine, and tangent of the angle, followed by their reciprocal functions: cosecant, secant, and cotangent. The process includes rationalizing the results and understanding the quadrant's impact on the sign of the functions.

What is the first step in finding trigonometric functions using a point on the terminal side of an angle?

• Find the reciprocal functions.

• Draw the angle in standard position.

• Calculate the hypotenuse of the triangle.

• Identify the quadrant where the point lies.

In which quadrant does the point (1, -1) lie?

• Quadrant IV

• Quadrant III

• Quadrant II

• Quadrant I

What type of triangle is formed when using the point (1, -1) to construct the angle?

• Equilateral triangle

• 30-60-90 triangle

• 45-45-90 triangle

• Scalene triangle

How do you calculate the sine of the angle using the triangle's sides?

• Adjacent side divided by hypotenuse

• Opposite side divided by hypotenuse

• Hypotenuse divided by opposite side

• Adjacent side divided by opposite side

What is the cosine of the angle if the adjacent side is 1 and the hypotenuse is √2?

• √2

• √2/2

• 1/√2

• 1

What is the tangent of the angle if the opposite side is -1 and the adjacent side is 1?

• 1

• -1

• 0

• Undefined

What is the cosecant of the angle if the sine is -√2/2?

• -√2

• √2

• -2/√2

• 2/√2

What is the secant of the angle if the cosine is √2/2?

• 1/√2

• √2

• 2/√2

• -√2

What is the cotangent of the angle if the tangent is -1?

• Undefined

• 0

• -1

• 1

Which of the following is a reciprocal function of sine?

• Secant

• Cosecant

• Tangent

• Cotangent