Sine and Cosine Rule

Front

What is the Sine Rule?

Back

The Sine Rule states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. It is expressed as: a/sinA = b/sinB = c/sinC.

Front

What is the Cosine Rule?

Back

The Cosine Rule relates the lengths of the sides of a triangle to the cosine of one of its angles. It is expressed as: c² = a² + b² - 2ab cosC.

Front

When do you use the Sine Rule?

Back

Use the Sine Rule when you have either two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA).

Front

When do you use the Cosine Rule?

Back

Use the Cosine Rule when you have either two sides and the included angle (SAS) or all three sides (SSS).

Front

What does SOH-CAH-TOA stand for?

Back

SOH-CAH-TOA is a mnemonic for remembering the definitions of sine, cosine, and tangent: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.

Front

What is the sine of 30 degrees?

Back

The sine of 30 degrees is 0.5.

Front

What is the cosine of 60 degrees?

Back

The cosine of 60 degrees is 0.5.

Front

What is the sine of 90 degrees?

Back

The sine of 90 degrees is 1.

Front

What is the cosine of 0 degrees?

Back

The cosine of 0 degrees is 1.

Front

How do you find the angle using the Sine Rule?

Back

To find an angle using the Sine Rule, rearrange the formula: sinA/a = sinB/b to solve for the angle: A = sin⁻¹(a * sinB/b).