Which of the following is equal to sin(270-x)?
A. -tan(x)
B. 1-tan(x)
C. -cos(x)
D. 1+cos(x)
E. 1+sin(x)
sin(270-x)=sin270cosx+cos270sinx
= -cosx + 0
Well, well, well, it seems like we've stumbled into the world of trigonometry! Let's unravel this mystery together, shall we?
To find the value of sin(270 - x), we can use an important trigonometric identity known as the cofunction identity. According to this identity, sin(theta) = cos(90 - theta).
In this case, if we apply the cofunction identity, we get sin(270 - x) = cos(90 - (270 - x)). By simplifying this expression, we get sin(270 - x) = cos(x).
So, the correct option out of the given choices is C. -cos(x).
Remember, math can be quite tricky, but with a little humor, it becomes a circus worth enjoying!
To find the value of sin(270-x), we can use the identity sin(A - B) = sin(A)cos(B) - cos(A)sin(B).
Let A = 270 and B = x. Substituting these values into the identity, we have:
sin(270 - x) = sin(270)cos(x) - cos(270)sin(x)
The sine of 270 degrees is -1, and the cosine of 270 degrees is 0. Substituting these values into the equation, we have:
sin(270 - x) = -1 * cos(x) - 0 * sin(x)
sin(270 - x) = -cos(x)
Therefore, the answer is option C. -cos(x).
To find the value of sin(270-x), we can use the trigonometric identity:
sin(270 - x) = sin(270) * cos(x) - cos(270) * sin(x)
First, let's determine the values of sin(270) and cos(270).
We know that the cosine and sine functions follow a repeating pattern every 360 degrees. Therefore, we can find sin(270) and cos(270) by considering their values at an equivalent angle within the first cycle.
270 degrees is equivalent to 270 - 360 = -90 degrees. At -90 degrees, the sine function is -1, and the cosine function is 0.
Now, substituting these values into the equation:
sin(270 - x) = -1 * cos(x) - 0 * sin(x) = -cos(x)
So, the correct answer is C. -cos(x).