91Ó°ÊÓ

The given angle is -840°. Since all trigonometric functions (sin, cos, tan) are periodic every 360°, they will have the same values at all angles which differ by whole number multiples of 360°. Hence, add 360° to -840° until we have an equivalent angle in the range of 0° to 360°: \(-840° + 2*360° = -120°\).

The negative angle of -120° takes us clockwise around the unit circle and it will end up in the second quadrant. This is equivalent to a positive rotation of 240° (since 360°-120° = 240°). Thus, we will find the sine, cosine, and tangent of 240°.

In the second quadrant, the sine is positive, the cosine is negative, and the tangent (which is sine divided by cosine) is also negative. We know that at 240° (or 180°+60°), the sine and cosine values are those for 60°, switched and with the sign determined by the quadrant. The sine of 240° is therefore \(-\frac{1}{2}\) (this is the sine of 60°, but it becomes negative because it's in the 3rd quadrant where sine is negative), the cosine of 240° is \(-\frac{\sqrt{3}}{2}\) (the cos of 60°, but negative because it's in the third quadrant where cosine is negative) and the tangent of 240°, which is \(\frac{sin(240°)}{cos(240°)}\), is \(\frac{1}{\sqrt{3}}\) (a positive divided by a negative is a negative, but in this case the negatives cancel since we're dividing two negatives and hence we get a positive result).