Six Trig Ratios

Front

What are the six trigonometric ratios?

Back

The six trigonometric ratios are: 1. Sine (sin) 2. Cosine (cos) 3. Tangent (tan) 4. Cosecant (csc) 5. Secant (sec) 6. Cotangent (cot)

Front

Define sine (sin) in terms of a right triangle.

Back

Sine (sin) is the ratio of the length of the opposite side to the length of the hypotenuse: sin(θ) = opposite/hypotenuse.

Front

Define cosine (cos) in terms of a right triangle.

Back

Cosine (cos) is the ratio of the length of the adjacent side to the length of the hypotenuse: cos(θ) = adjacent/hypotenuse.

Front

Define tangent (tan) in terms of a right triangle.

Back

Tangent (tan) is the ratio of the length of the opposite side to the length of the adjacent side: tan(θ) = opposite/adjacent.

Front

What is the relationship between sine and cosecant?

Back

Cosecant (csc) is the reciprocal of sine: csc(θ) = 1/sin(θ).

Front

What is the relationship between cosine and secant?

Back

Secant (sec) is the reciprocal of cosine: sec(θ) = 1/cos(θ).

Front

What is the relationship between tangent and cotangent?

Back

Cotangent (cot) is the reciprocal of tangent: cot(θ) = 1/tan(θ).

Front

How do you calculate cotangent using sine and cosine?

Back

Cotangent can be calculated as the ratio of cosine to sine: cot(θ) = cos(θ)/sin(θ).

Front

If sin(θ) = 3/5, what is csc(θ)?

Back

csc(θ) = 1/sin(θ) = 1/(3/5) = 5/3.

Front

If tan(θ) = 4/3, what is cot(θ)?

Back

cot(θ) = 1/tan(θ) = 3/4.