4.4 Find Any Angles using Trig

Front

What is the definition of secant (sec)?

Back

The secant of an angle θ in a right triangle is defined as the ratio of the length of the hypotenuse to the length of the adjacent side. It can also be expressed as sec(θ) = 1/cos(θ).

Front

How do you find the value of sec(θ) given a point on the terminal side?

Back

To find sec(θ) given a point (x, y) on the terminal side, first calculate the radius r using r = √(x² + y²). Then, use sec(θ) = r/x.

Front

What is the definition of cotangent (cot)?

Back

The cotangent of an angle θ is defined as the ratio of the length of the adjacent side to the length of the opposite side in a right triangle. It can also be expressed as cot(θ) = 1/tan(θ).

Front

How do you find cot(θ) given a point on the terminal side?

Back

To find cot(θ) given a point (x, y) on the terminal side, use cot(θ) = x/y.

Front

What is the definition of tangent (tan)?

Back

The tangent of an angle θ is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. It can also be expressed as tan(θ) = sin(θ)/cos(θ).

Front

How do you find tan(θ) given sin(θ) and cos(θ)?

Back

To find tan(θ), use the formula tan(θ) = sin(θ)/cos(θ).

Front

What is the definition of cosecant (csc)?

Back

The cosecant of an angle θ is defined as the ratio of the length of the hypotenuse to the length of the opposite side in a right triangle. It can also be expressed as csc(θ) = 1/sin(θ).

Front

How do you find csc(θ) given a point on the terminal side?

Back

To find csc(θ) given a point (x, y) on the terminal side, first calculate the radius r using r = √(x² + y²). Then, use csc(θ) = r/y.

Front

What are the signs of trigonometric functions in the different quadrants?

Back

In Quadrant I: all functions are positive. In Quadrant II: sin and csc are positive. In Quadrant III: tan and cot are positive. In Quadrant IV: cos and sec are positive.

Front

How do you determine the quadrant of an angle based on the signs of trigonometric functions?

Back

If tan(θ) < 0 and cos(θ) < 0, then θ lies in Quadrant II.