Solving Trig Equations - Extra Time

Why doesn't 2cosx − 3 = 0 have solutions?

• cos x is never bigger than one

• cos x is never equal to a fraction

• Actually, this equation does have a solution, x = π

• This equation will have a solution tomorrow.

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Which of these is equivalent to 2cos²x − 3cosx = 0 ?

• -cos²x = 0

• cosx(2cosx + 3) = 0

• cosx(2cosx − 3) = 0

• cos x = ⅔

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

Choose a good way to start solving this equation

tanx sin²x = 2 tanx

• divide tanx from both sides

• factor out tanx

• subtract 2 tanx from the left and then factor tanx out

• cancel sin²x out

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Factor 0 = sin²x − sinx

• 0 = sinx(sinx)

• 0 = sinx(1 − sinx)

• 0 = cosx(sinx − 1)

• 0 = sinx(sinx − 1)

Tags

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Factor: sec²x − secx − 2

• (sec x)(secx − 2)

• (secx − 2)(secx − 1)

• (secx − 2)(secx + 1)

• (secx + 2)(secx − 1)

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.B.2

CCSS.HSA.SSE.A.2

To solve the equation sec²x − secx = 2

• start by subtracting 2 from both sides and then factor

• add sec x to both sides and factor

• factor out secx and set each factor equal to 2

• sec x is never bigger than 1, so there are no solutions

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.4

csc²x = 2 is equivalent to sin²x = ½

• True

• False

Tags

CCSS.HSF.TF.C.8

Solve equation for  $0\le\theta<2\pi$  .
 $1=5-8\cos\theta$  

•  $\theta=\frac{\pi}{6},\frac{\pi}{3},\frac{11\pi}{6}$  

•  $\theta=\frac{\pi}{6},\frac{11\pi}{6}$  

•  $\theta=\frac{\pi}{6}$  

•  $\theta=\frac{\pi}{3},\frac{5\pi}{3}$  

Tags

CCSS.HSF.TF.A.1

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.3

CCSS.HSF.TF.A.4

Solve for all values of x over the interval [0,2π]

• $\frac{\pi}{6}\ and\ \frac{7\pi}{6}$

• $\frac{5\pi}{6}\ and\ \frac{11\pi}{6}$

• $\frac{\pi}{3}\ and\ \frac{5\pi}{3}$

• $\frac{2\pi}{3}\ and\ \frac{4\pi}{3}$

Solve equation for  $0\le\theta<2\pi$  .
 $-\sin\theta\csc\theta+3\csc\theta=\sqrt{2}\sin\theta+3\csc\theta$  

•  $\theta=\frac{5\pi}{4},\frac{11\pi}{6}$  

•  $\theta=\frac{3\pi}{4},\frac{7\pi}{6},\frac{7\pi}{4}$  

•  $\theta=0,\pi,\frac{5\pi}{4},\frac{7\pi}{4}$  

•  $\theta=\frac{5\pi}{4},\frac{7\pi}{4}$