Chapter Closure
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Exact value: - sqrt(3)/2
A reference angle of 30^(∘) gives a sine value of 0.5. However, as we can see from the diagram above, 180^(∘)-30^(∘)=150^(∘) will also result in a sine value of 0.5.
Multiply fractions
a/b=.a /3π./.b /3π.
Multiply
Let's draw this angle in the unit circle.
The angle 4π3 radians is a standard angle with an exact measurement.
As we can see, sin 4π3=- sqrt(3)2.
To determine which of these quadrants we should choose, we have to think about how we get a positive tangent. The tangent value of an angle is the ratio of an angles sine value to its cosine value. tan θ = sin θ/cos θ Since the cosine value is negative, the sine value must also be negative in order for the tangent to be positive. This means our angle must fall in the third quadrant. We can, for example, choose 240^(∘).
