Chapter Closure
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Since the sine of a trig expression is given by the vertical axis on the unit circle, we can find the exact value by identifying the y-value of the angle of rotation that corresponds to 60^(∘).
As we can see, sin 60^(∘) = sqrt(3)2.
As we can see, cos 180^(∘) = -1.
tan θ =sin θ/cos θ
Therefore, we have to identify both the cosine value and the sine value that corresponds to a rotation of 225^(∘).
As we can see, the cosine and sine value of 225^(∘) are both - 1sqrt(2). With this information, we can determine the tangent value. tan 225^(∘) = - 1/sqrt(2)/- 1/sqrt(2)=1
To find sin π4, we have to identify the y-coordinate when the angle of rotation is π4 radians.
As we can see, sin π4= 1sqrt(2).
As we can see, cos 2π3=- 12.
As we can see, the cosine and sine value of 3π2 are 0 and - 1, respectively. With this information, we can attempt to determine the tangent value. tan 3π/2= - 1/0 As we can see, tan 3π2 is undefined, as it results in dividing by 0.