Overview
1. Consider the right triangle ABC: Given AC = 12, AB = a, BC = b, and angle B = 90°
- Part I: Use the sine ratio to find the length of side b to two decimal places.
- Part II: Find the length of side a to two decimal places using the method of your choice.
2. Solve the triangle below by finding all missing sides and/or angles.
- Part I: Use the law of cosines to find the length of side AC. Round your answer to the nearest hundredth.
3. Graph the function y = −3 cos(2x) + 1
- Part I: What is the amplitude of this function?
- Part II: What is the vertical shift of this function?
- Part III: What is the period of this function?
- Part IV: Graph at least two periods of this function.
4. An object's motion is described by: d = 3 sin(8πt) − 2
- Part I: What is the object's position at t = 0?
- Part II: What is the object's maximum displacement from its t = 0 position?
- Part III: How much time is required for one oscillation?
- Part IV: What is the frequency of this oscillation?
5. Evaluate and explain each of the following:
a. cos⁻¹(cos(−π/6))
b. sin(tan⁻¹(4/3))
c. tan⁻¹(cos(π/2))
6. Solve: 2 sin x cos x − sin(2x) cos(2x) = 0
- Part I: Simplify using identity
- Part II: Factor
- Part III: Solve each factor
7. Vector Form and Dot Product
- Part II: Write vector v in polar form (|v|cosθ, |v|sinθ), where v = (−6, 13)
- Part III: Use dot product to check if vectors v = (−6, 13) and w = (−42, −34) are orthogonal
10. Find the fourth roots of the complex number z₁ = 1 + √3 i
- Part I: Write z₁ in polar form
- Part II: Find the modulus of the 4th roots
- Part III: Find the four angles for the 4th roots
- Part IV: Write the roots in rectangular form