Setting Up Trig Equations Pre 5.5

Front

What is the sine function in a right triangle?

Back

The sine function (sin) is defined as the ratio of the length of the opposite side to the length of the hypotenuse. For angle θ, it is given by: sin(θ) = opposite/hypotenuse.

Front

What is the cosine function in a right triangle?

Back

The cosine function (cos) is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. For angle θ, it is given by: cos(θ) = adjacent/hypotenuse.

Front

What is the tangent function in a right triangle?

Back

The tangent function (tan) is defined as the ratio of the length of the opposite side to the length of the adjacent side. For angle θ, it is given by: 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 sides involved. For example, for angle θ, if the opposite side is 'a' and the hypotenuse is 'c', the equation is: sin(θ) = a/c.

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 sides involved. For example, for angle θ, if the adjacent side is 'b' and the hypotenuse is 'c', the equation is: cos(θ) = b/c.

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 sides involved. For example, for angle θ, if the opposite side is 'a' and the adjacent side is 'b', the equation is: tan(θ) = a/b.

Front

What is the relationship between sine and cosine?

Back

The sine and cosine functions are related through the Pythagorean identity: sin²(θ) + cos²(θ) = 1.

Front

What is the formula for finding the opposite side using sine?

Back

To find the opposite side 'a' using sine, rearrange the sine equation: a = c * sin(θ), where 'c' is the hypotenuse.

Front

What is the formula for finding the adjacent side using cosine?

Back

To find the adjacent side 'b' using cosine, rearrange the cosine equation: b = c * cos(θ), where 'c' is the hypotenuse.

Front

What is the formula for finding the opposite side using tangent?

Back

To find the opposite side 'a' using tangent, rearrange the tangent equation: a = b * tan(θ), where 'b' is the adjacent side.