Solving Trig equations #2

 $\sin^2x-1+\cos^2x+\tan x=-1$  Solve for x including the entire unit circle

•  $\frac{3\pi}{4},\frac{5\pi}{4}$  

•  $\frac{\pi}{2},\frac{3\pi}{2}$  

•  $\frac{3\pi}{4},-\frac{\pi}{4}$  

•  $\frac{3\pi}{2}$  

Which of the following is NOT
a solution to
sin θ = √(3) / 2 ?

• π / 3
• 2π / 3
• 5π / 3
• 7π / 3

Solve on the domain [0, 2π)
cos² x + sin x + 1 = 0

• π
• 3π/2
• π/6, 5π/6, 3π/2
• No solution

To solve this equation, cos²x + sinx = 1, replace cos²x with

• 1/(sec²x)

• sin²x − 1

• 1 − sin²x

• 1 + tan²x

Which of these are equal to 1? (Check all that apply)

• sin²(θ) + cos²(θ)

• sec²(θ) - tan²(θ)

• csc²(θ) - cot²(θ)

• tan²(θ) - cos²(θ)

 $\frac{\tan\left(\theta\right)}{\cot\left(\theta\right)}\equiv$  

•  $1$  

•  $\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$  

•  $\tan^2\left(\theta\right)$  

•  $\sec^2\left(\theta\right)$  

 $\tan^2x+\sec x=1\ \ \ \ \ \ \ 0\le x\le\pi$  

•  $x=0,\ \pi$  

•  $x=0,\ \pi,\ \frac{5\pi}{6}$  

• no solution

•  $x=0,\frac{2\pi}{3}$  

 $\cos^2\theta=\sin^2\theta\ \ \ \ \ \ \ \ \ \ \ 0\le\theta<2\pi$  

•  $x=\frac{\pi}{4},\ -\frac{\pi}{4}$  

•  $x=\frac{\pi}{4},\frac{3\pi}{4}$  

•  $x=\frac{\pi}{4},\ \frac{3\pi}{4},\ \frac{5\pi}{4},\ -\frac{\pi}{4}$  

•  $x=0,\frac{\pi}{4},\ \frac{3\pi}{4}$  

 $\tan\ x\ +\ \sqrt{3}=0$  

•  $x\ =\ \frac{2\pi}{3}$  

•  $x=\frac{2\pi}{3},-\frac{\pi}{3}$  

•  $x=\frac{\pi}{3}$  

•  $x=\frac{4\pi}{3}$  

 $\tan^2\ x=3$  

•  $x=\frac{\pi}{3},\ \ \frac{4\pi}{3}$  

•  $x=\frac{\pi}{6},\ \frac{5\pi}{6}$  

•  $x=\frac{\pi}{3},\frac{2\pi}{3},\frac{4\pi}{3},-\frac{\pi}{3}$  

• None of these