Flashcard No. 7.1-7.2 in Geometry (Trigonometric Ratios )

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: \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \)

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: \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \)

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: \( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \)

Front

How do you determine which trigonometric ratio to use?

Back

To determine which trigonometric ratio to use, identify the sides of the triangle you know and the side you need to find. Use Tangent if you have opposite and adjacent, Sine if you have opposite and hypotenuse, and Cosine if you have adjacent and hypotenuse.

Front

What is the formula to find the angle using the Tangent Ratio?

Back

To find the angle using the Tangent Ratio, use the inverse tangent function: \( \theta = \tan^{-1}\left(\frac{\text{opposite}}{\text{adjacent}}\right) \)

Front

If the opposite side is 3 and the adjacent side is 4, what is the Tangent Ratio?

Back

The Tangent Ratio is \( \tan(\theta) = \frac{3}{4} = 0.75 \)

Front

What is the relationship between the three trigonometric ratios?

Back

The three trigonometric ratios (Sine, Cosine, Tangent) are related through the Pythagorean identity: \( \sin^2(\theta) + \cos^2(\theta) = 1 \) and \( \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} \)

Front

How do you set up an equation to solve for a variable using trigonometric ratios?

Back

To set up an equation, identify the known sides and the angle, then use the appropriate trigonometric ratio to express the unknown side in terms of the known sides.

Front

What is the value of \( \tan(45^\circ) \)?

Back

The value of \( \tan(45^\circ) = 1 \)

Front

If you know the angle and one side, how can you find the other sides?

Back

You can use the trigonometric ratios to find the other sides. For example, if you know the angle and the opposite side, use Sine to find the hypotenuse and Tangent to find the adjacent side.