How do you solve? <span title="Tan(arccos(sin-60)))=cot(x)?">Tan(arccos(sin-60)))=cot(...</span>

Question

How do you solve? Tan(arccos(sin-60)))=cot(...

Answer 1

tan(acos(sin(-60))) = cot(x)

sin(-60) = -√3/2

tan(acos(-√3/2)) = cot(x)

acos(-√3/2) = 5π/6

tan(5π/6) = cot(x)

tan(5π/6) = -√3/3

-√3/3 = 1/tan(x)

-3/√3 = tan(x)

x = -π/3

Answer: -π/3 or -60 degrees

no calculator reqd.

Answer 2

Tan(arccos(sin(-60))) = cot(x)

Use your computers calculator.

Click START &gt; All Programs &gt; Accessories &gt; Calculator

Switch to scientific view, if necessary. Make sure Degrees is selected.

Enter 60, then click on the +/- button to change it to -60.

Click the sin button.

Click in the check box at the top that says Inv.

Click the cos button.

Click the tan button.

Click the Inv check box.

Click the tan button.

x = -30

Answer 3

What is &quot;sin-60&quot;? Did you mean sin(60)? Or sin (60°)? Because they&#039;re very different.

Once you settle on that, I&#039;d suggest taking the tangent of both sides to isolate x, then using a calculator to find the value. Because I don&#039;t think it&#039;ll be easy to find the value of:

tan(tan(arccos(sin(60°))))

By hand/mentally.

-IMP ;) :)