Step 2 - Trig Lab Assignment Worksheet.sagews

#Line 1-11 blank.

Evaluate the following using SAGE. Use the show command to make the output "pretty".

1. All 6 trig functions on 5π/6

2. All 6 trig function on 9π/2

3. sin^-1(-.5)

4. Solve sin(θ)=-.75 for θ

5. Solve tan(φ)=100 for φ

#Complete the above problems in the space below
#1.All 6 trig functions on 5π/6
show([sin(5*pi/6),cos(5*pi/6),tan(5*pi/6),csc(5*pi/6),sec(5*pi/6),cot(5*pi/6)])

[$\displaystyle \frac{1}{2}$, $\displaystyle -\frac{1}{2} \, \sqrt{3}$, $\displaystyle -\frac{1}{3} \, \sqrt{3}$, $\displaystyle 2$, $\displaystyle -\frac{2}{3} \, \sqrt{3}$, $\displaystyle -\sqrt{3}$]

#2.All 6 trig function on 9π/2 
show([sin(9*pi/2),cos(9*pi/2),tan(9*pi/2),csc(9*pi/2),sec(9*pi/2),cot(9*pi/2)])

[$\displaystyle 1$, $\displaystyle 0$, $\displaystyle \infty$, $\displaystyle 1$, $\displaystyle \infty$, $\displaystyle 0$]

#3.sin-1(-.5)
show(asin(-.5))







#4.Solve sin(θ)=-.75 for θ
theta=var('theta')
solve(sin(theta)==-.75,theta)
show(solve(sin(theta)==-.75,theta))

[theta == -arcsin(3/4)]

[$\displaystyle \theta = -\arcsin\left(\frac{3}{4}\right)$]

#5.Solve tan(φ)=100 for φ
phi=var('phi')
solve(tan(phi)==100,phi)
show(solve(tan(phi)==100,phi))

[phi == arctan(100)]

[$\displaystyle \phi = \arctan\left(100\right)$]