8-1

M=tan(alpha). The slope of the line is m. Alpha is also known as angle of inclination.

Tan 2(theta)= b/a-c which finds the alpha of a conic ax^2+bxy+cy^2...=

Solve

Ex. 1. 4 sin theta=3
First divide both sides by 4
Theta= sin^-1 3/4 which is 48.590 degrees
Sin is positive so it's in the first and second quadrant. To move to the second quadrant make it negative and add 180 which gives you 131.41. You must then convert them to degrees minutes seconds. So to put 48.590 in that form first multiply .590 by 60 which gives you 35' then multiply .4 by 60 which gives you 24". And 131.41 in that form multiply .41 by 60 which gives you 41' and then .6 by 60 which gives you 36. So the final answer is 48 degrees 35' 24" and 131 degrees 24' 36".

2. 2 tan theta+1=0
Subtract 1 then divide both sides by 2. Theta= tan^-1(-1/2) which gives you 26.565 degrees. Tan is negative so its in the 2nd and 4th quadrant. To move it to the 2nd quadrant make -ve and +180 which gives you 153.435 degrees. To move to the 4th quadrant make -ve and +360 which gives you 333.435. Now convert to degrees minuets seconds and your final answer is 153 degrees 26' 6" and 333 degrees 26' 6".