Question

Find the exact value of cos210 using the unit circle

Answer 1

i have no idea how to use the unit circle for this is there another way?

Answer 2

The output values for Cosine are the same as the output values for Sine except they're pi/2 radians (90 degrees) out-of-phase. in other words, Cosine is just like Sine if you shift the input up by 90 degrees first before using the Sine function. Alternatively, Sine is just like Cosine if you shift the input down by 90 degrees before using the Cosine function. \[Sin (\Theta + 90^{o}) = Cos( \Theta )\] Or, \[Sin ( \Theta ) = Cos ( \Theta - 90^{o})\] So, if you know the Sine values for the unit circle, you just have to shift them up by 90 degrees to find the Cosine values: \[Cos(210^{o}) = Sin(300^{o})\]

Answer 3

cos(570) = cos(570 - 360) = cos(210)

From the unit circle(which is easy to construct) :

cos(210) = -sqrt(3)/2

Answer 4

210 is in the third quadrant so sine and cosine are negative, also 210-180=30dedrees therefore,
cos 210=-cos(210-180)=-cos 30=\[-\sqrt{3}/2 ans\]