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
show(sin(5*pi/6))

$\displaystyle \frac{1}{2}$

show(cos(5*pi/6))

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

show(tan(5*pi/6))

$\displaystyle -\frac{1}{3} \, \sqrt{3}$

show(sec(5*pi/6))

$\displaystyle -\frac{2}{3} \, \sqrt{3}$

show(csc(5*pi/6))

$\displaystyle 2$

show(cot(5*pi/6))

$\displaystyle -\sqrt{3}$

#Q2.

show(sin(9*pi/2))

$\displaystyle 1$

show(cos(8*pi/2))

$\displaystyle 1$

show(tan(9*pi/2))

$\displaystyle \infty$

show(sec(9*pi/2))

$\displaystyle \infty$

show(csc(9*pi/2))

$\displaystyle 1$

show(cot(9*pi/2))

$\displaystyle 0$

#Q3
(sin(-0.5))^-1

-2.08582964293349

#Q4
theta=var('theta')
solve(sin(theta)==-0.75,theta)
show(solve(sin(theta)==-0.75,theta))

[theta == theta]

[$\displaystyle \theta = \theta$]

#Q5
theta=var('theta')
solve(tan(theta)==100,theta)
show(solve(tan(theta)==100,theta))

[theta == arctan(100)]

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