Cosine Ratio

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 represented as: \( \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} \)

Front

How do you calculate the cosine of an angle?

Back

To calculate the cosine of an angle, use the formula: \( \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} \). Measure the lengths of the adjacent side and the hypotenuse, then divide the length of the adjacent side by the length of the hypotenuse.

Front

What is the cosine of 0 degrees?

Back

The cosine of 0 degrees is 1, which means that when the angle is 0, the length of the adjacent side is equal to the length of the hypotenuse.

Front

What is the cosine of 90 degrees?

Back

The cosine of 90 degrees is 0, indicating that at this angle, the length of the adjacent side is 0.

Front

If the adjacent side is 4 units and the hypotenuse is 5 units, what is the cosine of the angle?

Back

Using the cosine ratio: \( \cos(\theta) = \frac{4}{5} \). Therefore, \( \cos(\theta) = 0.8 \).

Front

What is the relationship between cosine and the unit circle?

Back

In the unit circle, the cosine of an angle corresponds to the x-coordinate of the point on the circle at that angle.

Front

What is the cosine of 45 degrees?

Back

The cosine of 45 degrees is \( \frac{\sqrt{2}}{2} \) or approximately 0.707.

Front

How does the cosine function behave in different quadrants?

Back

In the first quadrant, cosine is positive; in the second quadrant, it is negative; in the third quadrant, it is negative; and in the fourth quadrant, it is positive.

Front

What is the cosine of an angle in a right triangle with sides 3, 4, and 5?

Back

The cosine of the angle opposite the side of length 3 is \( \cos(\theta) = \frac{4}{5} \).

Front

What is the cosine rule?

Back

The cosine rule states that for any triangle: \( c^2 = a^2 + b^2 - 2ab \cos(C) \), where \( c \) is the side opposite angle \( C \), and \( a \) and \( b \) are the other two sides.