Worksheet 6
Precalculus
1 Questions
- For the triangle at the bottom, suppose that \(a=2\) and \(c=3\). Evaluate \(u\) in radians.
- Find the angle between a side of length 6 and the side with length 10 in an isosceles triangle that has one sie of length 10 and two sides of length 6.
- Find \(\cos(\sin^{-1}(2/3))\) exactly.
- Suppose that \(t\) is such that \(\sin^{-1}t =3\pi/8\). Evaluate:
- \(\sin^{-1}(-t)\)
- \(\cos^{-1}t\)
- \(\cos^{-1}(-t)\).
- Find the area of a parallelogram that has pairs of sides of lengths 4 and 10, with \(\pi/6\) radian angle between two of those sides.
- Suppose a triangle has area 6 with sides of lengths 3 and 8. Find the angle between those two sides.
- Suppose the triangle at the bottom is not a right triangle, but the third
angle is labeled as \(w\). If \(a=5, b=6\), and \(c=9\), evaluate:
- \(u\)
- \(v\)
- \(w\).
- Suppose the triangle at the bottom is not a right triangle, but the third
angle is labeled as \(w\). If \(a=4, b=3\), and \(u = 30^\circ\), evaluate:
- \(v\) (two answers)
- \(w\)
- \(c\).
- Assume that \(u,v \in (\pi/2,\pi)\), and that \(\sin u = 1/5\) and \(\sin v
= 1/6\). Find:
- \(\cos u\)
- \(\cos(2u)\)
- \(\sin(2u)\)
- \(\cos(v/2)\)
- \(\sin(v/2)\)
- Find \(\sin(\pi/8)\) exactly using half or double angle formulas.
- Find \(\cos(15^\circ)\) exactly using addition or subtraction formulas.
- Find a formula for \(\cos (\theta + \pi/4)\).
- Let \(f(x) = 5 \cos(\pi x)\).
- Sketch the graph of \(h\) on the interval \([-4,4]\), labeling 5 points, all of which are in the same period.
- What is the amplitude of \(h\)?
- What is the period of \(h\)?
- What is the range of \(h\)?
- What is the phase shift of \(h\)?
- What is the vertical translation of \(h\)?
- Let \(g(x) \) be the function derived from moving \(\cos(x)\) down 4 units, right 1 unit, scaled in the vertical direction by a factor of 3, and has a phase shift of \(\pi/6\) to the right. What is a formula for \(g(x)\)?