1. If the terminal side of a 330 degree angle intersects a unit circle, what would the coordinates at the point of intersection? The angle 330° is conterminal with the an angle of -30° in the fourth quadrant. It forms a triangle with the hypotenuse of 1 X coordinate is equal to the cosine of -30° Y coordinate is equal to the sine of -30° So the coordinates are (√3/2, -1/2) 2. Solve for x: 3 + cos 2x = 7/2; only include answers on [0, 2π] 3 + cos 2x = 7/2 Subtract 3 from both sides Cos 2x = 1/2 Cosine function is positive in st adn 4rt quadrant So the angles are π/3 and 5π/3 Now, we go around unit circle twice because our angle is 2x Adding 2π or 6π/3 to each angle 7π/3 and 11π/3 Divide them by 2 Angles that satisfy the equation are π/6 5π/6 7π/3 11π/3 3. Verify the following identity by using an angle sum identity: cos (2x) = 1 – 2(sin2x). Hint (2x = x + x) Using the angle sum formula, cos(x+x) = cosxcosx - sinxsinx = cos2x - sin2x. cos2x + sin2x = 1, rearrage it cos2x = 1 - sin2x. Putting this in place of cos2x in our expression, we get cos2x = 1-sin2x-sin2x = 1 - 2sin2x

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