Calculating Theta: Solving Sin Theta = 3/8 for 2 Possible Answers

[graycolor]

Okay I need to find theta...Sin theta is equal to 3/8. I just need someone to put this in a calculator for me as I do not have a powerful enough calculator, decimals are fine too, you should be able to find 2 answers from 0 to 2pi. This is a small part in a greater more complicated problem.

Using Arcsin I was only able to find only one answer there should be another one.

 

[Office_Shredder]

No calculator is going to spit out two answers for arcsin(theta). If you draw the unit circle, and look at an example of an angle, you should be able to find the other angle with the same value of sin(theta) and figure out what the formula for it is based on the other solution you have

 

[ElectroPhysics]

sin(theta) = 3/8 which implies
theta = arcsin(3/8)
theta1 = 0.3843967 + 2(pie)(n) where n= plus minus(0, 1, 2 etc)
now as theta1 is upward in first quadrant thus theta2 will be in 2nd quadrant
theta2 = pie - 0.3843967 thus
theta2 = 2.7571958 + 2(pie)(n) where n= plus minus(0,1,2 etc)

put n = 0, 1, 2 etc and find range
for the range of 0 to 2pie the answer is
theta1 = 0.3843967
theta2 = 2.7571958