Simplify the expression using the half-angle identity


1. Solve the given equation graphically, 2 sin 2x = x^2 + 1

2. The vertical displacement y (in m) of the end of a robot arm is given below. Find the first four values of t (in s) for which y = 0. y y = 1.7 cos 0.1t - 1.55 sin 0.2t

3. Solve the given trigonometric equation analytically and by use of graphing calculator. Use values of x for 0 or < x <2pi. 100 cos^2 x- 50 =0

4. Find all solution in the interval [0, 2pi). sin 2x cosx - sinx =0.

5. In finding the path of a sliding particle, the expression sqrt. 12.5 - 12.5 cos theta is used. Simplify this expression using a half-angle identity.

6. Verify each identity by comparing the graph of the left side with the graph of the right side on a graphing calculator. 2 csc (2x) tan x = cos(2x)

7. Find the exact value of sin 180 degree using the function of 90 degree.

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Mathematics: Simplify the expression using the half-angle identity
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