Which statement is ALWAYS true?

A)
The sine of an angle is equal to the sine of the angle's complement.

B)
The cosine of an angle is equal to the sine of the angle's supplement.

C)
The sine of an angle is equal to the cosine of the angle's complement.

D)
The cosine of an angle is equal

3 answers

If you know your trig relations and formulas, then its clearly C

otherwise, you could test them with some angles.
Remember, if you find even one exception to a mathematical rule, then that rule is invalid
A, let Ø = 20, then its complement is 70°
sin20 = appr .342
sin70 = appr .94 , so it is NOT A

B) cos20 = appr .94 (mmm, wasn't that sin70° ???)
sin 160 = .342 , so NOT B

C)
sin20 = .342
cos70 = .342 , mmmhhh?

let's take a really weird angle
sin 37.1234° = .603533676 -- on my calculator
cos(90 - 37.1234)
= cos( 52.8766) = .603533676
well, what are the chances of that ???

Sure looks like C

of course, if you haven't already learned,
sin Ø = cos(90°-Ø) for any value of Ø

your D is not complete

Thanks.

thanks