Math  /  Trigonometry

Question5. Solve each equation in the specified domain. a) 3cosθ1=4cosθ,0θ<2π3 \cos \theta-1=4 \cos \theta, 0 \leq \theta<2 \pi b) 3tanθ+1=0,πθ2π\sqrt{3} \tan \theta+1=0,-\pi \leq \theta \leq 2 \pi c) 2sinx1=0,360<x360\sqrt{2} \sin x-1=0,-360^{\circ}<x \leq 360^{\circ} d) 3sinx5=5sinx43 \sin x-5=5 \sin x-4, 360x<180-360^{\circ} \leq x<180^{\circ} e) 3cotx+1=2+4cotx3 \cot x+1=2+4 \cot x, 180<x<360-180^{\circ}<x<360^{\circ}

Studdy Solution
Solve the equation 3cotx+1=2+4cotx3 \cot x + 1 = 2 + 4 \cot x for 180<x<360-180^\circ < x < 360^\circ.
1. Rearrange to isolate cotx\cot x:
3cotx+1=2+4cotx 3 \cot x + 1 = 2 + 4 \cot x 12=4cotx3cotx 1 - 2 = 4 \cot x - 3 \cot x 1=cotx -1 = \cot x
2. Solve for xx where cotx=1\cot x = -1.
3. The solutions in the specified domain are x=135,315,45x = 135^\circ, 315^\circ, -45^\circ.
The solutions for each equation are: a) θ=π\theta = \pi b) θ=π6,5π6,7π6,11π6\theta = -\frac{\pi}{6}, \frac{5\pi}{6}, \frac{7\pi}{6}, \frac{11\pi}{6} c) x=45,135,315,225x = 45^\circ, 135^\circ, -315^\circ, -225^\circ d) x=30,150,210,330x = -30^\circ, -150^\circ, -210^\circ, -330^\circ e) x=135,315,45x = 135^\circ, 315^\circ, -45^\circ

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord