Final answer:
The statement that sin(T) equals cos(T) for a 44° angle in a right triangle is never true. It would only be true if ∠T were 45°, which is the only angle where the opposite and adjacent sides are equal, making the sine and cosine ratios identical.
Step-by-step explanation:
The statement that if ∠T is a 44° angle in a right triangle, then sin(T)=cos(T) is sometimes true. This is because the sine and cosine functions are not equal, but they can be equal in certain cases. To understand when this is true, we need to look at the values of sine and cosine for different angles.
The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. In a right triangle, the hypotenuse is the longest side, the side opposite the right angle, and the adjacent side is the side adjacent to the angle of interest.
For a 44° angle in a right triangle, the sine of the angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. The cosine of the angle is the ratio of the length of the adjacent side to the length of the hypotenuse. In general, the sine and cosine of different angles are not equal, but they can be equal for specific angles. For example, in a right triangle with a 45° angle, the sine and cosine are equal because the lengths of the opposite and adjacent sides are the same.
To summarize, the statement that if ∠T is a 44° angle in a right triangle, then sin(T)=cos(T) is sometimes true.