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(51/2*sqrt(2)/6))

$\displaystyle \sin\left(\frac{17}{4} \, \sqrt{2}\right)$

show(cos(51/2*sqrt(2)/(6)))

$\displaystyle \cos\left(\frac{17}{4} \, \sqrt{2}\right)$

show(csc(51/2*sqrt(2)/(6)))

$\displaystyle \csc\left(\frac{17}{4} \, \sqrt{2}\right)$

show(tan(51/2*sqrt(2)/(6)))

$\displaystyle \tan\left(\frac{17}{4} \, \sqrt{2}\right)$

show(sec(51/2*sqrt(2)/(6)))

$\displaystyle \sec\left(\frac{17}{4} \, \sqrt{2}\right)$

show(cot(51/2*sqrt(2)/(6)))

$\displaystyle \cot\left(\frac{17}{4} \, \sqrt{2}\right)$

show(cos(91/2*sqrt(2)/(2)))

$\displaystyle \cos\left(\frac{91}{4} \, \sqrt{2}\right)$

show(sin(91/2*sqrt(2)/(2)))

$\displaystyle \sin\left(\frac{91}{4} \, \sqrt{2}\right)$

show(tan(91/2*sqrt(2)/(2)))

$\displaystyle \tan\left(\frac{91}{4} \, \sqrt{2}\right)$

show(csc(91/2*sqrt(2)/(2)))

$\displaystyle \csc\left(\frac{91}{4} \, \sqrt{2}\right)$

show(cot(91/2*sqrt(2)/(2)))

$\displaystyle \cot\left(\frac{91}{4} \, \sqrt{2}\right)$

show(sec(91/2*sqrt(2)/(2)))

$\displaystyle \sec\left(\frac{91}{4} \, \sqrt{2}\right)$

show(asin(-.5))

$\displaystyle -0.523598775598299$

theta=var('theta')
ans=solve(sin(theta)==-.75,theta)
ans

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

theta=var('theta')
ans=solve(tan(theta)==100,theta)
ans

[theta == arctan(100)]