University:
York University
Course:
MATH 1013 | Applied Calculus
Academic year:

2023
Views:

34

Pages:

1
Author:

Niklas

III. Trigonometric Equations FIRST DEGREE EQUATIONS (Ch.5) I. FIRST DEGREE EQUATIONS ↳ solve similar to a linear equation. Solve 4sinx+5=7 for x ∈ [0, 360°) [4 sinx=2] [sinx=\frac{1}{2}] ISOLATE TRIG FUNCTION (x=sin^{-1}(\frac{1}{2})) EMPLOY INVERSE TRIG [x=30^{\circ}] note that (sinx>0) in quadrants I and II. 30 is in quad. I, so there is another solution in quad II. Solution therefore, the other is 150 {30, 150° this solution is on [0,300); however, we can provide a general solution on (-0,00) by [{(30+360m)^{\circ},(150^{\circ}+300n)^{\circ}}.n\in\mathbb{Z}] solve (4cosx+5=7) for (x=[0,2\pi)) 2. solve (2cosx+7=3) for x = [0, 360°) [4 cosx=2] [5 cosx=-4] [cosx=\frac{1}{2}] [x=cos^{-1}(\frac{1}{2})] [x=\frac{\pi}{3}] [cosx=\frac{-7}{5}] 145 [x=143^{\circ}] II IV solve (7tanx=2\sqrt{3}) tanx for xe (-00,00) 4. solve (\frac{1}{2}(secx+3)=secx+\frac{5}{2}for~x\in[0,2\pi)) [1\sqrt{3}] [tanx=\frac{45}{3}] secx=-2 I I [x=tan^{-1}(\frac{\sqrt{3}}{5})] [x=sec^{-1}(-2)] [x=\frac{4\pi}{6}] [x=\frac{2\pi}{3}] IN II IV (X=\frac{\pi}{6}+\pi n) πε