Question

evaluate the following without using a calculator.
7. arccot(sqrt3/3)
8. arcsec(2)

Answer 1

So in number 7, there isn't a type-0?

For number 8,
let y=arcsec(2)
So
sec(y)=2
=> cos(y)=1/2
When is cos(y)=1/2?

Answer 2

Use unit circle.

Answer 3

\(\bf cot^{-1}\left(\frac{\sqrt{3}}{3}\right)\implies \theta\implies cot(\theta)=\left(\frac{\sqrt{3}}{3}\right)\\ \quad \\
tan(\theta)=\left(\frac{3}{\sqrt{3}}\right)\implies tan(\theta)=\sqrt{3}\)


notice the value is positive, and the constraints of the inverse cotangent function will put it in the 1st Quadrant

Answer 4

thanks !

Answer 5

Oh for number 7 you could make a right triangle and figure out and look at cosine and evaluate arccot(sqrt(3)/3) that way.