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
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
To determine which statement is always true, we can analyze each option one by one:
A) The sine of an angle is equal to the sine of the angle's complement.
To determine if this statement is always true, let's consider an example:
Let's say the angle is 30 degrees. The complement of 30 degrees is 60 degrees.
The sine of 30 degrees is 0.5, and the sine of 60 degrees is also 0.5.
So, in this case, the statement is true. However, it is not true for all angles. For example, if the angle is 45 degrees, the complement is 45 degrees as well, and their sines are not equal. Therefore, option A is not always true.
B) The cosine of an angle is equal to the sine of the angle's supplement.
Similarly, let's consider an example to evaluate this statement:
Let's say the angle is 45 degrees. The supplement of 45 degrees is 135 degrees.
The cosine of 45 degrees is approximately 0.707, and the sine of 135 degrees is also approximately 0.707.
So, in this case, the statement is true. However, it is not true for all angles. For example, if the angle is 30 degrees, the supplement is 150 degrees, and their cosines and sines are not equal. Therefore, option B is not always true.
C) The sine of an angle is equal to the cosine of the angle's complement.
Following the same approach, let's examine this statement:
Let's say the angle is 30 degrees. The complement of 30 degrees is 60 degrees.
The sine of 30 degrees is 0.5, and the cosine of 60 degrees is also 0.5.
Thus, in this case, the statement is true. Similar to option A, this statement is not always true for all angles. For example, if the angle is 45 degrees, the complement is 45 degrees as well, and their sines and cosines are not equal. Therefore, option C is not always true.
D) The cosine of an angle is equal...
This statement is incomplete and undefined. It does not provide the necessary information to evaluate its truthfulness.
Based on this analysis, we can conclude that none of the given statements (A, B, C, or D) are always true.