Question

3cos315-2sin210 in surd form

Answer 1

[AI-generated answer — Bot]

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.

Answer 2

AAAaannndd the bot gets it wrong yet again!

nope -- cos315 = +1/√2

Answer 3

[AI-generated answer — Bot]

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.

Answer 4

[AI-generated answer — Explain Bot]

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.