07/10 Trigonometric Foundations Free Online FlashCards

What do positive and negative angles indicate?

A positive angle rotates counterclockwise, while a negative angle rotates clockwise.

How is radian measure defined?

A radian is θ = s/r, where s is intercepted arc length and r is circle radius.

How do you convert between degrees and radians?

Use 180° = π radians. Thus, multiply degrees by π/180 to convert to radians, or radians by 180/π to convert to degrees.

What are coterminal angles?

Coterminal angles have the same initial and terminal sides and differ by an integer multiple of 360° or 2π radians.

What equation defines the unit circle?

The unit circle is centered at (0,0), has radius 1, and satisfies x² + y² = 1.

How does the unit circle define sine and cosine?

The point is (cos θ, sin θ), so cos θ is the x-coordinate and sin θ is the y-coordinate.

Where is tangent positive or negative?

Tangent is positive in Quadrants I and III and negative in Quadrants II and IV.

What is a reference angle?

A reference angle is the acute positive angle between a terminal side and the x-axis.

What are the three primary right-triangle ratios?

For an acute angle, sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, and tan θ = opposite/adjacent.

What are the reciprocal identities?

csc θ = 1/sin θ, sec θ = 1/cos θ, and cot θ = 1/tan θ.

What is the primary Pythagorean identity?

sin² θ + cos² θ = 1.

Which basic trigonometric functions are even or odd?

Sine and tangent are odd: sin(−θ) = −sin θ and tan(−θ) = −tan θ. Cosine is even: cos(−θ) = cos θ.