Is this statement always, sometimes, or never true?If ∠N and ∠P are complementary angles, then cos(N)=cos(P).
Question
Is this statement always, sometimes, or never true?If ∠N and ∠P are complementary angles, then cos(N)=cos(P).
Solution
The statement is never true. Here's why:
Complementary angles are two angles whose measures add up to 90 degrees. If ∠N and ∠P are complementary, then their measures could be any two numbers that add up to 90. For example, ∠N could be 30 degrees and ∠P could be 60 degrees.
The cosine of an angle in a right triangle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. Therefore, the cosine of an angle depends on the measure of the angle.
If ∠N is 30 degrees, then cos(N) is approximately 0.866. If ∠P is 60 degrees, then cos(P) is approximately 0.5. Therefore, cos(N) does not equal cos(P).
So, the statement "If ∠N and ∠P are complementary angles, then cos(N)=cos(P)" is never true.
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