1) Find the exact value of the expression:

Question

tan−1(tan(−120651/47π))... How do you find Tan(-120651/47pi)? I don't know how to find exact values, if it's not a recognizable value.

2)Find a simplified expression for tan(sin−1(a/5))...

Because tan = y/x and sin(y/r) can be sin-1(y/r)(i think)

First i did sqrt(5^2-a^2) so i have x

so i did (a^2)/sqrt(5^2-a^2)... I don't know how to do the next step or if i did it right.

3)Solve sin(x)=−0.89 on 0≤x<2π

There are two solutions, A and B, with A < B
1st solution= 4.239

For the first solution all i did was sin-1(-.89)=-1.9073 then i did pi-(-1.9073)to get me 4.2389. And i think that solution is from the 3rd quadrant... and i don't know how to find the other solution...

Answer 1

120651/47 π = 2567.04 π
So, tan(-120651/47 π)
= -tan(120651/47 π)
= -tan(2567π + 2/47π)
= -tan(2/47 π)
arctan(-tan(2/47 π)) = -2/47 π

You are correct. x = a/√(25-a^2)
son tan(arcsin(a/5)) = a/√(25-a^2)

Always use the reference angle from QI.
arcsin(0.89) = 1.097
sin is negative is QIII and QIV
So, your two solutions are π+1.097 and 2π-1.097

Answer 2

1a5. Find tan theta.