Question

Solve each equation on the interval 0θ<2π0 \leq \theta<2 \pi. tanθ+3=secθ\tan \theta+\sqrt{3}=\sec \theta

Solution

Verified
Answered 2 years ago
Answered 2 years ago
Step 1
1 of 8

First, we simplify the equation by expressing it in terms of sines and cosines.

tanθ+3=secθtanθ+3secθ=0sinθcosθ+31cosθ=0sinθ1cosθ+3=0sinθ1cosθ+3=0sinθ1cosθ+3cosθcosθ=0sinθ1+3cosθcosθ=0\begin{aligned} \tan \theta + \sqrt{3} &= \sec \theta \\ \tan \theta + \sqrt{3} - \sec \theta &= 0\\ \frac{\sin \theta}{\cos\theta} + \sqrt{3} - \frac{1}{\cos \theta} &= 0\\ \frac{\sin \theta-1}{\cos\theta} + \sqrt{3} &= 0\\ \frac{\sin \theta-1}{\cos\theta} + \sqrt{3} &= 0\\ \frac{\sin \theta-1}{\cos\theta} + \frac{\sqrt{3}\cos\theta}{\cos\theta} &= 0\\ \frac{\sin \theta-1+\sqrt{3}\cos\theta}{\cos\theta} &= 0\\ \end{aligned}

Create a free account to view solutions

Create a free account to view solutions

Recommended textbook solutions

Precalculus 2nd Edition by Carter, Cuevas, Day, Malloy

Precalculus

2nd EditionISBN: 9780076602186Carter, Cuevas, Day, Malloy
8,885 solutions
Precalculus Enhanced with Graphing Utilities 7th Edition by Michael Sullivan

Precalculus Enhanced with Graphing Utilities

7th EditionISBN: 9780134119281Michael Sullivan
10,040 solutions
Nelson Functions 11 1st Edition by Chris Kirkpatrick, Marian Small

Nelson Functions 11

1st EditionISBN: 9780176332037Chris Kirkpatrick, Marian Small
1,275 solutions
Precalculus with Limits 3rd Edition by Larson

Precalculus with Limits

3rd EditionISBN: 9781133962885 (3 more)Larson
11,422 solutions

More related questions

1/4

1/7