Is this statement always, sometimes, or never true?If ∠C is an acute angle, then sin(C)=cos(C).
Question
Is this statement always, sometimes, or never true?If ∠C is an acute angle, then sin(C)=cos(C).
Solution
The statement "If ∠C is an acute angle, then sin(C)=cos(C)" is sometimes true. This is only true when ∠C is 45 degrees. In a right triangle, if one of the acute angles is 45 degrees, then the sine and cosine of that angle are equal. This is because in a 45-45-90 triangle, the two legs are of equal length, so the ratio of the length of the side opposite the angle to the length of the hypotenuse (which is the definition of sine) is the same as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse (which is the definition of cosine). However, for any other acute angle, the sine and cosine values will not be equal.
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