Is this statement always, sometimes, or never true?If m∠X and m∠Y sum to 90° and m∠X is a 45° angle, then sin(X)=cos(Y).
Question
Is this statement always, sometimes, or never true?If m∠X and m∠Y sum to 90° and m∠X is a 45° angle, then sin(X)=cos(Y).
Solution
This statement is always true. Here's why:
Step 1: The problem states that m∠X and m∠Y sum to 90°. This means that the angles are complementary.
Step 2: In trigonometry, the sine of an angle is equal to the cosine of its complement. This is known as the co-function identity.
Step 3: Given that m∠X is a 45° angle, m∠Y would be 45° as well because they sum to 90°.
Step 4: Therefore, sin(45°) = cos(45°), which means sin(X) = cos(Y).
So, the statement "If m∠X and m∠Y sum to 90° and m∠X is a 45° angle, then sin(X)=cos(Y)" is always true.
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