Is this statement always, sometimes, or never true?If ∠Q is a 45° angle, then cos(Q)=sin(Q).
Question
Is this statement always, sometimes, or never true?If ∠Q is a 45° angle, then cos(Q)=sin(Q).
Solution
The statement "If ∠Q is a 45° angle, then cos(Q)=sin(Q)" is always true. Here's why:
Step 1: Understand the trigonometric functions of sine and cosine. In a right triangle, the sine of an angle is the length of the opposite side divided by the length of the hypotenuse. The cosine of an angle is the length of the adjacent side divided by the length of the hypotenuse.
Step 2: Apply these definitions to a 45° angle in a right triangle. In a 45-45-90 triangle (a special type of right triangle), the sides opposite and adjacent to the 45° angle are of equal length.
Step 3: Therefore, the sine and cosine of a 45° angle are equal because they are both the length of the same side divided by the length of the hypotenuse.
So, cos(45°) = sin(45°) = 1/√2 or approximately 0.707. Hence, the statement is always true.
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