Write the following trigonometric expression in terms of sine and cosine. Express your answer in terms of $x$ only.

$\frac{1+\tan (-x)}{\cot (-x)}$

Rewrite the given trigonometric expression using either a sum or difference identity for cosine.

cos(9π/16)cos(5π/16) + sin(9π/16)sin(5π/16)

Use a product-to-sum formula to write the given trigonometric expression as a sum or difference:

2 cos 55° sin 150°

Solve the following trigonometric equation on the interval [0, 2π) with the help of an identity.

sin 3x cos x - cos 3x sin x = (√3)/2

Identify whether the following measurements of two sides and an angle can produce one triangle, two triangles, or no triangle. Find the missing side lengths and angles of the triangle. Express the lengths and angles in one decimal place.

a = 5.3, b = 3, A = 155°

Find the missing side length and angles of the triangle. Express the length to one decimal place and the angle to the nearest degree.

A vector b starts at M and ends at N. Express the vector b in terms of i and j.

M = (-3, 15), N = (-4, -4)

Find the magnitude and direction angle of the vector a given below. Express your answer to one decimal place.

$a=(31i-17j)-(25i-17j)$

Given the following vector, $\mathbf{v}$, obtain the unit vector that aligns with the direction of $\mathbf{v}$.

$\mathbf{v}=-\mathbf{i}-\sqrt3\mathbf{j}$

Two vectors a and b are given. Determine the dot products a ⋅ b and a ⋅ a:

a = i, b = 18j

Plot the given polar coordinates on a polar coordinate system. 

(5, 60°)