Question

1. Decide whether the statement below is true or false. Then fully explain why. The triangle below can b used to help with your explanation if needed.

"The sine of any acute angle is equal to the cosine of its complementary angle."[help me plzz!!]​

Answer 1

Answer: True

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Work Shown:

sin(angle) = opposite/hypotenuse

sin(alpha) = MN/NP

sin(alpha) = y/z

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cos(angle) = adjacent/hypotenuse

cos(beta) = MN/NP

cos(beta) = y/z

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Both sin(alpha) and cos(beta) are equal to y/z, so that means sin(alpha) = cos(beta). This is true because alpha+beta = 90, ie the angles are complementary.

Similarly, you should find that sin(beta) and cos(alpha) are both equal to x/z, which is further proof that the statement is true.