We use the fact that:
- tan(240) = tan(240 - 180) = -tan(60) = -sqrt(3)
- cos(120) = -cos(120 - 360) = -cos(240) = -1/2
So, we have:
2 tan 240 + 3 cos120 = 2(-sqrt(3)) + 3(-1/2)
= -2sqrt(3) - 3/2
= (-4sqrt(3) - 6)/2
= -2(2sqrt(3) + 3)/2
= -(2sqrt(3) + 3)
Evaluate 2 tan 240 + 3 cos120 leaving your answer in a surd form
2 answers
First, we need to find the values for tan(240) and cos(120):
240 degrees is in the third quadrant where both cosine and sine values are negative. To find the values, we can subtract 240 - 180 = 60. So tan(240) = -tan(60).
tan(60) is known to be √3, therefore tan(240) = - √3.
120 degrees is in the second quadrant where only sine values are positive. To find the values, we can subtract 180 - 120 = 60. So cos(120) = -cos(60).
cos(60) is known to be 1/2, therefore cos(120) = - 1/2.
Now we can plug these values back into the expression:
2 * (-√3) + 3 * (-1/2) = -2√3 - 3/2.
240 degrees is in the third quadrant where both cosine and sine values are negative. To find the values, we can subtract 240 - 180 = 60. So tan(240) = -tan(60).
tan(60) is known to be √3, therefore tan(240) = - √3.
120 degrees is in the second quadrant where only sine values are positive. To find the values, we can subtract 180 - 120 = 60. So cos(120) = -cos(60).
cos(60) is known to be 1/2, therefore cos(120) = - 1/2.
Now we can plug these values back into the expression:
2 * (-√3) + 3 * (-1/2) = -2√3 - 3/2.