Mathematics

Question

What is the relationship between the sine and cosine of complementary angles and why is the relationship true?

2 Answer

  • Hello!


    The sine of any acute angle is equal to the cosine of its complement. The cosine of any acute angle is equal to the sine of its complement. of any acute angle equals its cofunction of the angle's complement. Yes, there is a "relationship" regarding the tangent of the two acute angles (A and B) in a right triangle.

    Hope this Helps! :)
  • Complementary angles sum up to 90 degrees. The relationship between the sine and cosine of complementary angles is that they are equal.

    Angles A and B are complementary if:

    [tex]A + B = 90[/tex]

    Make A the subject:

    [tex]A = 90 - B[/tex]

    Take sin of A

    [tex]\sin(A) = \sin(90 - B)[/tex]

    Apply sine formula to expand

    [tex]\sin(A) = \sin(90) \cos(B) - \sin(B)\cos(90)[/tex]

    Substitute values for sin(90) and cos(90)

    [tex]\sin(A) = 1 \times \cos(B) - \sin(B) \times 0[/tex]

    [tex]\sin(A) = \cos(B)[/tex] --- this is why the relationship is true:

    The above shows that the relationship between the sine and cosine of complementary angles as equals.

    Read more about complementary angles at:

    https://brainly.com/question/3027144

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