SOLUTION: Please help me work out sec(sin-1(3/4)

Question 245585: Please help me work out
sec(sin-1(3/4)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
This can be done using a calculator but you have to know how and even then you will only get a decimal approximation of the exact answer.

We can do this without calculators fortunately. sin-1(3/4) represents an angle whose sin is 3/4. Let's draw a picture of such an angle. (Note: the drawing is not to scale.)

A is the angle whose sin is 3/4. Note how the opposite side is 3 and the hypotenuse is 4. This makes the sin 3/4! To find the sec of A we need the adjacent side, x. To find x we can use the Pythogorean Theorem:

Sec is hypotenuse over adjacent so
sec(sin-1(3/4) =
This is the exact answer. But normally we do not leave square roots in denominators so we will multiply the numerator and denominator by :
sec(sin-1(3/4) =
sec(sin-1(3/4) =
which is the exact answer with a rational denominator.

RELATED QUESTIONS
Please help me figure out sin(sin^-1... (answered by Alan3354)

Please help me solve 6 tan pi/4 plus sin pi/3 sec... (answered by Alan3354)

Simplify (sec-tan)(1+sin) Please help! I can't figure this problem out! (answered by JellyBeans)

Prove: 1)sec^2x(1-sin^2x)=1 2)sinxcosxtanx=1-cos^2x 3)(cotx/cscx)=cosx... (answered by drk)

Please help me prove these following identities with explanation, thanks <3 1.) {{{... (answered by Alan3354)

I have three questions that I need extreme help on. 1. Find sec thata if sin theta=-4/5 (answered by midwood_trail,solver91311)

Please help me verify this equation: (sec x +tan x) (1-sin x) = cos... (answered by lwsshak3)

please help me. what is _________1_________________ = sin theta cot theta sec... (answered by Theo,greenestamps)

Please help me to solve this question Sin(60+A)�sin(60-A)=1/4[3-4... (answered by greenestamps)