Maths Help

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Is the answer 0.8660 or -0.8660 ?

And second question, a bit simpler, but how the fuck do I make this into a diagram?

" Draw a diagram (including the unit circle) which shows that cos(-Θ°)=cosΘ° "

Its asking for sin theta not theta.
If costheta is 0.5 costheta squared is 0.25
1-0.25 = sintheta squared.
0.75 = sintheta squared
Answer is sqr root of 0.75 which is +- 0.8660

>>8630199
Thank you!
I got to 0.8660 in my working, does sin^-1 make the answer +-0.8660 ?

>>8630199
Wrong.

Every real number has 1 and only 1 square root. It is also always greater than or equal to 0.

>>8630204
So 25=5^2 , but not 25=(-5)^2 ?

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>>8630193
is something like this an acceptable response?

>>8630204
What?

>>8630193
Draw a unit circle (radius of 1)

Now draw an arbitrary angle. It will be easier to see if you draw the angle in the first quadrant of that circle. Label that angle [math]\theta[/math]
Now draw [math]-\theta[/math], which just means draw the same angle except it's clockwise from the horizontal rather than counterclockwise. You are now aware that [math]\cos{\theta} = \cos{{-\theta}}[/math], since cosine is the horizontal part of the right triangle which forms on the unit circle.

>>8630209
I would not use an angle of 0, since obviously +- 0 are actually the same angle. Choose something less than greater 0 and less than 90 degrees for simplicity.

>>8630202
No its +- because a positive numbers square root can be positive or negative.
E.g 25 = 5 × 5 and 25 = -5 x -5
So square root of 25 is +- 5

>>8630217
>Choose something less than greater 0 and less than 90 degrees for simplicity.

Typo. Meant to say choose an angle [math]0^\circ < \theta < 90^\circ[/math]

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>>8630223
>>8630217

OK what about this?

>>8630227
Good, just draw an angle of -45 degrees now. You will see that the two triangles share a common side on the x-axis. Since cosine(theta) = adjacent/hypotenus, and the adjacent sides of both angle are equal, and the hypotenus is equal, it's clear that cos(theta) = cos(-theta) = adjacent/hypotenus

>>8630227

Haha. You are so close. The triangle you drew is theta. Now you should draw one for negative theta in the 4th quadrant.

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>>8630235
>>8630231
am I retarded or is this correct?

>>8630239
Yes, but you should label the angles.

>>8630208
>>8630215
Square root specifically means a function that returns a positive 2nd order root.

I never said a negative number squared isn't positive.

Every polynomial degree 2 has 2 roots but the square root is a function that only returns the positive. Look it up.