Question

1. what are the si units?
2. in the triangle below, list all the trigonometric relationships between the labeled sides & angles.
3. match the following physical quantities to their corresponding fundamental quantities, where l is length, t is time, and m is mass, then write their units in the si system.

physical quantity fundamental quantity si unit
force lt^(-2)
area l^3
velocity ml^(-3)
volume mlt^(-2)
acceleration lt^(-1)
density l^2

Explanation:

1.

The International System of Units (SI) is the modern - form of the metric system. It has seven base units: the meter (m) for length, the kilogram (kg) for mass, the second (s) for time, the ampere (A) for electric current, the kelvin (K) for thermodynamic temperature, the mole (mol) for amount of substance, and the candela (cd) for luminous intensity.

Step1: Define sine

$\sin\theta=\frac{A}{C}$

Step2: Define cosine

$\cos\theta=\frac{B}{C}$

Step3: Define tangent

$\tan\theta=\frac{A}{B}$

Step4: Define cosecant

$\csc\theta=\frac{C}{A}$

Step5: Define secant

$\sec\theta=\frac{C}{B}$

Step6: Define cotangent

$\cot\theta=\frac{B}{A}$

Step1: Force

Force $F = ma$ (Newton's second law), where $m$ is mass and $a$ is acceleration. Acceleration $a=\frac{\text{change in velocity}}{\text{time}}$, so its dimensions are $[L][T]^{- 2}$. Mass has dimension $[M]$. Then the dimension of force is $[M][L][T]^{-2}$ and its SI unit is the newton (N), where $1\ N = 1\ kg\cdot m/s^{2}$.

Step2: Area

Area of a two - dimensional shape. Its dimension is $[L]^{2}$ and its SI unit is the square meter ($m^{2}$).

Step3: Velocity

Velocity $v=\frac{\text{displacement}}{\text{time}}$, so its dimension is $[L][T]^{-1}$ and its SI unit is the meter per second ($m/s$).

Step4: Volume

Volume of a three - dimensional object. Its dimension is $[L]^{3}$ and its SI unit is the cubic meter ($m^{3}$).

Step5: Acceleration

Acceleration $a=\frac{\text{change in velocity}}{\text{time}}$, so its dimension is $[L][T]^{-2}$ and its SI unit is the meter per second squared ($m/s^{2}$).

Step6: Density

Density $
ho=\frac{m}{V}$, where $m$ is mass and $V$ is volume. So its dimension is $[M][L]^{-3}$ and its SI unit is the kilogram per cubic meter ($kg/m^{3}$).

Answer:

The seven SI base units are the meter (m) for length, kilogram (kg) for mass, second (s) for time, ampere (A) for electric current, kelvin (K) for thermodynamic temperature, mole (mol) for amount of substance, and candela (cd) for luminous intensity.

2.