91Ó°ÊÓ

Approximate the area of a parallelogram that has sides of lengths \(a\) and \(b\) (in feet) if one angle at a vertex has measure \(\boldsymbol{\theta}\). $$a=12.0, \quad b=16.0, \quad \theta=40^{\circ}$$

Express the complex number in trigonometric form with \(0 \leq \theta<2 \pi\) $$-5-3 i$$

Approximate the area of a parallelogram that has sides of lengths \(a\) and \(b\) (in feet) if one angle at a vertex has measure \(\boldsymbol{\theta}\). $$44 a=40.3, \quad b=52.6, \quad \theta=100^{\circ}$$

Express the complex number in trigonometric form with \(0 \leq \theta<2 \pi\) $$-2-7 i$$

Approximate the horizontal and vertical components of the vector that is described. A quarterback releases a football with a speed of \(50 \mathrm{ft} / \mathrm{sec}\) at an angle of \(35^{\circ}\) with the horizontal.

Express the complex number in trigonometric form with \(0 \leq \theta<2 \pi\) $$4-3 i$$

Vectors are used extensively in computer graphics to perform shading. When IIght strikes a nat surface, it is reflected, and that area should not be shaded. Suppose that an incoming ray of IIght is represented by a vector L and that \(N\) is a vector orthogonal to the nat surface, as shown in the figure. The ray of reflected light can be represented by the vector \(\mathbf{R}\) and is calculated using the formula \(\mathbf{R}=2(\mathbf{N} \cdot \mathbf{L}) \mathbf{N}-\mathbf{L} .\) Compute \(\mathbf{R}\) for the vectors \(\mathbf{L}\) and \(\mathbf{N}\) (Figure can't copy) $$\mathbf{L}=\left\langle-\frac{4}{5}, \frac{3}{5}\right\rangle, \quad \mathbf{N}=\langle 0,1\rangle$$

Approximate the horizontal and vertical components of the vector that is described. A child pulls a sled through the snow by exerting a force of 20 pounds at an angle of \(40^{\circ}\) with the horizontal.

Vectors are used extensively in computer graphics to perform shading. When IIght strikes a nat surface, it is reflected, and that area should not be shaded. Suppose that an incoming ray of IIght is represented by a vector L and that \(N\) is a vector orthogonal to the nat surface, as shown in the figure. The ray of reflected light can be represented by the vector \(\mathbf{R}\) and is calculated using the formula \(\mathbf{R}=2(\mathbf{N} \cdot \mathbf{L}) \mathbf{N}-\mathbf{L} .\) Compute \(\mathbf{R}\) for the vectors \(\mathbf{L}\) and \(\mathbf{N}\) (Figure can't copy) $$\mathbf{L}=\left\langle\frac{12}{13},-\frac{5}{13}\right\rangle, \quad \mathbf{N}=\left\langle\frac{1}{2} \sqrt{2}, \frac{1}{2} \sqrt{2}\right\rangle$$

Express the complex number in trigonometric form with \(0 \leq \theta<2 \pi\) $$1-3 i$$