Sin, Cos and Tan

Front

What are the definitions of sine, cosine, and tangent in a right triangle?

Back

Sine (sin) is the ratio of the length of the opposite side to the hypotenuse. Cosine (cos) is the ratio of the length of the adjacent side to the hypotenuse. Tangent (tan) is the ratio of the length of the opposite side to the adjacent side.

Front

How do you calculate the sine of an angle?

Back

To calculate the sine of an angle, use the formula: sin(angle) = opposite side / hypotenuse.

Front

How do you calculate the cosine of an angle?

Back

To calculate the cosine of an angle, use the formula: cos(angle) = adjacent side / hypotenuse.

Front

How do you calculate the tangent of an angle?

Back

To calculate the tangent of an angle, use the formula: tan(angle) = opposite side / adjacent side.

Front

What is the relationship between sine, cosine, and tangent?

Back

The relationship is given by the identity: tan(angle) = sin(angle) / cos(angle).

Front

What is the Pythagorean theorem and how does it relate to sine, cosine, and tangent?

Back

The Pythagorean theorem states that in a right triangle, a² + b² = c², where c is the hypotenuse. This theorem is used to find the lengths of sides when calculating sine, cosine, and tangent.

Front

What is the opposite side in relation to an angle in a right triangle?

Back

The opposite side is the side that is directly across from the angle in question.

Front

What is the adjacent side in relation to an angle in a right triangle?

Back

The adjacent side is the side that is next to the angle in question and is not the hypotenuse.

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

How do you set up a trigonometric equation to solve for a side in a right triangle?

Back

Identify the known sides and angles, then use the appropriate trigonometric ratio (sin, cos, or tan) to set up the equation.