Find the exact value, in radians, of the expression.
sin -1(√2/2)

Question

Find the exact value, in radians, of the expression.
sin -1(√2/2)

jim_thompson5910 · Answer

Hint: use a unit circle http://www.math.ucsd.edu/~jarmel/math4c/Unit_Circle_Angles.png

anonymous · Answer

How do i tell which side is the sin?

jim_thompson5910 · Answer

the y coordinate of any point on the unit circle is equal to sin(theta)

jim_thompson5910 · Answer

example: 

sin(60) = sqrt(3)/2 because the point at 60 degrees has sqrt(3)/2 as the y coordinate

sin(pi/3) = sqrt(3)/2 ... same reason as above (just in the angle is now in radians)

anonymous · Answer

$$5\pi/4$$?

anonymous · Answer

Ok...thanks thats makes sense!!

jim_thompson5910 · Answer

there's one before that in quadrant 1

jim_thompson5910 · Answer

what you see is in quadrant 2

jim_thompson5910 · Answer

technically you are correct, but they want the principal value

jim_thompson5910 · Answer

oh wait, you said 5pi/4 when it should be 3pi/4

anonymous · Answer

yes! Thanks

jim_thompson5910 · Answer

anyways, take a look at the angle and point I circled


You'll see the answer is actually pi/4

anonymous · Answer

So if tan^-1 0 would be 3pi/2?

jim_thompson5910 · Answer

no tan is undefined at pi/2 and 3pi/2

jim_thompson5910 · Answer

but tan is zero when theta = 0 or theta = pi

so that's why tan^-1(0) = 0

anonymous · Answer

Interesting...you explain this so much easier than my professor

jim_thompson5910 · Answer

glad you're understanding it