Setting up trig equations

Front

What is the sine ratio in a right triangle?

Back

The sine ratio is defined as the ratio of the length of the opposite side to the length of the hypotenuse. It is expressed as: sin(θ) = opposite/hypotenuse.

Front

What is the cosine ratio in a right triangle?

Back

The cosine ratio is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. It is expressed as: cos(θ) = adjacent/hypotenuse.

Front

What is the tangent ratio in a right triangle?

Back

The tangent ratio is defined as the ratio of the length of the opposite side to the length of the adjacent side. It is expressed as: tan(θ) = opposite/adjacent.

Front

How do you set up a sine equation for a right triangle?

Back

To set up a sine equation, identify the angle and the lengths of the opposite side and the hypotenuse. Use the formula: sin(θ) = opposite/hypotenuse.

Front

How do you set up a cosine equation for a right triangle?

Back

To set up a cosine equation, identify the angle and the lengths of the adjacent side and the hypotenuse. Use the formula: cos(θ) = adjacent/hypotenuse.

Front

How do you set up a tangent equation for a right triangle?

Back

To set up a tangent equation, identify the angle and the lengths of the opposite side and the adjacent side. Use the formula: tan(θ) = opposite/adjacent.

Front

What is the relationship between sine and cosine?

Back

The relationship between sine and cosine can be expressed as: sin(θ) = cos(90° - θ). This means that the sine of an angle is equal to the cosine of its complementary angle.

Front

What is the Pythagorean identity involving sine and cosine?

Back

The Pythagorean identity states that for any angle θ: sin²(θ) + cos²(θ) = 1.

Front

How can you find the value of x using sine?

Back

To find x using sine, set up the equation: sin(θ) = opposite/hypotenuse, and solve for x if it represents either the opposite or hypotenuse.

Front

How can you find the value of x using cosine?

Back

To find x using cosine, set up the equation: cos(θ) = adjacent/hypotenuse, and solve for x if it represents either the adjacent or hypotenuse.