CHAPTER 17. TRIGONOMETRY 17.4
This is the general solution. Notice that we added the 10 ◦and divided by 2 only at the end. Noticethat
we added (180◦. n) because the tangent hasa period of 180 ◦. This is also divided by 2 in the last step
to keep the equation balanced. We chose quadrants I and III because tan was positive and we used
the formulae θ in quadrant I and (180◦+θ) in quadrant III. To find solutions where− 360 ◦< x < 360 ◦
we substitute integers for n:
- n = 0; x = 39, 1 ◦; 219 , 1 ◦
- n = 1; x = 129, 1 ◦; 309 , 1 ◦
- n = 2; x = 219, 1 ◦; 399 , 1 ◦(too big!)
- n = 3; x = 309, 1 ◦; 489 , 1 ◦(too big!)
- n =− 1 ; x =− 50 , 9 ◦; 129 , 1 ◦
- n =− 2 ; x =− 140 , 9 ◦;− 39 , 9 ◦
- n =− 3 ; x =− 230 , 9 ◦;− 50 , 9 ◦
- n =− 4 ; x =− 320 , 9 ◦;− 140 , 9 ◦
- n =− 5 ; x =− 410 , 9 ◦;− 230 , 9 ◦
- n =− 6 ; x =− 500 , 9 ◦;− 320 , 9 ◦
Solution: x =− 320 , 9 ◦;− 230 ◦;− 140 , 9 ◦;− 50 , 9 ◦;39, 1 ◦;129, 1 ◦;219, 1 ◦and 309 , 1 ◦
Linear Trigonometric Equations EMBDJ
Just like with regular equations without trigonometric functions, solving trigonometric equations can
become a lot more complicated. You should solve these just like normal equations to isolate a single
trigonometric ratio. Then you follow the strategyoutlined in the previoussection.
Example 11:
QUESTIONWrite down the generalsolution for 3cos(θ− 15 ◦)− 1 =− 2 , 583