Question 459727: Using the two special triangles and your knowledge of angles of any magnitude, find the exact value of:(a)sin 2pi/3
b) cos 2pi/3
c) tan 7pi/6
If f(x) = sin x ,g(x) = cos2x and h(x) = tan3x, find, correct to three significant figures:(a)f(1) + g(1) + h(1)
b) f(g(h(1)))
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Refer to the unit circle. When you plot 2pi/3, you will see that the y-coordinate is sqrt(3)/2 and the x-coordinate is -1/2. These correspond to sine and cosine, respectively, so we have sin(2pi/3) = sqrt(3)/2 and cos(2pi/3) = -1/2. That's all you need for parts a and b.
Try c) using the same method. Of course you will have to find both x- and y- coordinates to evaluate tangent, but you can still use the 30-60-90 triangle. And for the last question you will need a calculator.
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