trig question?

Question

I am having some trouble with 2 different trig problems. Can someone lend me a hand?

1.) arcsin [sin Pi/6] (they want an exact answer)

2.) write the following as an algebraic expression.

tan [sec-1 u/5 ] (*the -1 is actually an inverse sine)


I am unable to reach my professor and would really appreciate any help! Thank you!

Answer 1

for #1, the sin and arcsin reverse each other, so the answer is pi/6. done!

for #2), draw your right triangle. Focus on one of the angles and label for the secant (hypotenuse/adjacent) the u and the 5. Now you have two of the three sides of a right triangle and can find the third side by using the Pythagorean Thm. You should determine that the opposite side is u2-25.
NOW, you can write the tangent as (u2-25)/u. done!

Answer 2

1. arcsin [sin X] is just X. This reads the angle whose sine is the sine of X.

So this is just pi/6 which is just 30 degrees

2. the angle whose secant is u/5
since secant = 1/cos then the cos is 5/u
If you put this information into a right triangle, the side opposite the angle in question is SQRT(u^2 - 25) (think about the cosine - it is 5 over u and remember that a^2 + b^2 = c^2 and a=5 and c=u)

So the tan is SQRT(u^2 - 25)/25

Answer 3

use a calculater