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3cos315-2sin210 in surd form
Bot
answered
First, we note that:
cos 315 = cos (360 - 45) = -cos 45 = -1/√2
sin 210 = sin (180 + 30) = -sin 30 = -1/2
Therefore:
3cos315 - 2sin210 = 3(-1/√2) - 2(-1/2)
= -3/√2 + 1
= (-3 + √2)/√2
So the answer in surd form is (-3 + √2)/√2.
oobleck
answered
AAAaannndd the bot gets it wrong yet again!
nope -- cos315 = +1/√2
Bot
answered
I apologize for the earlier mistake. You are correct that cos 315 = +1/√2. Therefore,
3cos315 - 2sin210 = 3(1/√2) - 2(-1/2)
= 3/√2 + 1
= (3 + √2)/√2
So the answer in surd form is (3 + √2)/√2.
Explain Bot
answered
To express the expression 3cos(315°) - 2sin(210°) in surd form, we need to find the exact values of cosine and sine for these angles.
First, let's find the value of cos(315°):
cos(315°) can be derived from the unit circle. In the unit circle, 315° lies in the fourth quadrant, where the x-coordinate is negative and the y-coordinate is positive. The value of cos(315°) is therefore -√2/2.
Next, let's find the value of sin(210°):
sin(210°) can also be derived from the unit circle. In the unit circle, 210° lies in the third quadrant, where both the x-coordinate and the y-coordinate are negative. The value of sin(210°) is therefore -√3/2.
Now, let's substitute these values back into the original expression:
3cos(315°) - 2sin(210°)
= 3 * (-√2/2) - 2 * (-√3/2)
= -3√2/2 + √3
Therefore, the expression 3cos(315°) - 2sin(210°) in surd form is -3√2/2 + √3.