Tutor profile: Alex L.

Solve for $$x$$ (in radians), if $$x=arcsin(\frac{\sqrt{3}}{2} )$$?

Solution: $$x=arcsin(\frac{\sqrt{3}}{2} )=sin^{ - 1} (\frac{\sqrt{3}}{2})$$ $$sin(x)=\frac{\sqrt{3}}{2}$$ Using the 30-60-90 triangle on a unit-circle, when $$x=60^{\circ} \, (\pi/3 \, radians)$$, the value of $$sin(\pi/3)=\frac{\sqrt{3}}{2}$$ $$x=\pi/3\, radians$$

John is riding his bike at a speed of 4.5 m/s. As he nears his destination, he increases his speed from 4.5 m/s to 8.5 m/s in 12 seconds. What is his average rate of acceleration?

Solution: John's average rate of acceleration is $$\frac{v_f-v_i}{t} = \frac{8.5-4.5\,m/s}{12\,s} = 0.33\,m/s^2$$

Show the steps that you would take to evaluate the following expression $$5x + 2y/3$$ when $$x = 5$$ and $$y=6$$.

Solution: $$5x+2y/3 = 5(5)+2(6)/3= 25+12/3 = 25+4 = 29$$