Solve sin ⁡ x = − 1 \sin x=-1 sin x = − 1 on the interval [ 0 , 2 π ) \left[0,2\pi\right) [ 0 , 2 π )

x = 3 π 2 x=\frac{3\pi}{2} x = 2 3 π

x = π 2 , 3 π 2 x=\frac{\pi}{2\ },\ \frac{3\pi}{2} x = 2 π , 2 3 π

x = π 2 x=\frac{\pi}{2} x = 2 π

What is a good first step to solving this equation? 5 cos ⁡ x − 3 = 3 cos ⁡ x 5\cos x-\sqrt{3}=3\cos x 5 cos x − 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> = 3 cos x

Subtract 3 cos ⁡ x 3\cos x 3 cos x from both sides of the equation

Add 3 cos ⁡ x 3\cos x 3 cos x to both sides of the equation

What is a good next step to solving this equation? 2 cos ⁡ x − 3 = 0 2\cos x-\sqrt{3}=0 2 cos x − 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> = 0

Add 3 \sqrt{3} 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> to both sides of the equation

Subtract 3 \sqrt{3} 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> from both sides of the equation

Divide both sides of the equation by cos ⁡ x \cos x cos x

Check all solutions to this equation cos ⁡ x = 3 2 \cos x=\frac{\sqrt{3}}{2} cos x = 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

11 π 6 + 2 n π \frac{11\pi}{6}+2n\pi 6 1 1 π + 2 n π

π 6 + 2 n π \frac{\pi}{6}+2n\pi 6 π + 2 n π

π 3 + 2 n π \frac{\pi}{3}+2n\pi 3 π + 2 n π

2 π 3 + 2 n π \frac{2\pi}{3}+2n\pi 3 2 π + 2 n π

Which of these has the same solution as csc ⁡ x − 2 = 0 \csc x-2=0 csc x − 2 = 0

sin ⁡ x = 1 2 \sin x=\frac{1}{2} sin x = 2 1

cos ⁡ x = 1 2 \cos x=\frac{1}{2} cos x = 2 1

sin ⁡ x = 2 \sin x=2 sin x = 2

sin ⁡ x = − 1 2 \sin x=-\frac{1}{2} sin x = − 2 1

To find the general solution to a trig equation, you should add what to the solutions for sine and cosine equations?

Nothing, you found the solutions

Find the general solution(s) of the equation. 2 cos ⁡ x − 1 = 0 \sqrt{2}\cos\ x\ -1=0 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> cos x − 1 = 0

π 4 + 2 π n , 7 π 4 + 2 π n \frac{\pi}{4}+2\pi n\ \ \ \ ,\ \ \ \frac{7\pi}{4}+2\pi n 4 π + 2 π n , 4 7 π + 2 π n

π 4 + 2 π n \frac{\pi}{4}+2\pi n 4 π + 2 π n

π 4 + 2 π n , 3 π 4 + 2 π n \frac{\pi}{4}+2\pi n\ \ \ \ ,\ \ \ \frac{3\pi}{4}+2\pi n\ 4 π + 2 π n , 4 3 π + 2 π n

3 π 4 + 2 π n , 5 π 4 + 2 π n \frac{3\pi}{4}+2\pi n\ \ \ \ ,\ \frac{5\pi}{4}+2\pi n 4 3 π + 2 π n , 4 5 π + 2 π n

3 sin ⁡ x + 1 = sin ⁡ x 3\sin\ x\ +\ 1\ =\ \sin\ x 3 sin x + 1 = sin x

x = 7 π 6 + 2 π n , x = 11 π 6 + 2 π n x=\frac{7\pi}{6}+2\pi n,\ \ \ x\ =\ \frac{11\pi}{6}+2\pi n x = 6 7 π + 2 π n , x = 6 1 1 π + 2 π n

x = π 6 + 2 π n , x = 5 π 6 + 2 π n x=\frac{\pi}{6}+2\pi n,\ \ \ x\ =\ \frac{5\pi}{6}+2\pi n x = 6 π + 2 π n , x = 6 5 π + 2 π n

x = 4 π 3 + 2 π n , x = 5 π 3 + 2 π n x=\frac{4\pi}{3}+2\pi n,\ \ \ \ x=\frac{5\pi}{3}+2\pi n x = 3 4 π + 2 π n , x = 3 5 π + 2 π n

x = π 4 + π n x=\frac{\pi}{4}+\pi n x = 4 π + π n

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

cos x is never equal to a fraction

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

This equation will have a solution tomorrow.

Solve equation for 0 ≤ θ < 2 π 0\le\theta<2\pi 0 ≤ θ < 2 π . 4 + 4 tan ⁡ θ = 0 4+4\tan\theta=0 4 + 4 tan θ = 0

θ = 3 π 4 , 7 π 4 \theta=\frac{3\pi}{4},\frac{7\pi}{4} θ = 4 3 π , 4 7 π

θ = 7 π 4 \theta=\frac{7\pi}{4} θ = 4 7 π

θ = 0 , 3 π 4 \theta=0,\frac{3\pi}{4} θ = 0 , 4 3 π

3 sin ⁡ x + 1 = sin ⁡ x 3\sin\ x\ +\ 1\ =\ \sin\ x 3 sin x + 1 = sin x

x = 7 π 6 + 2 π n , x = 11 π 6 + 2 π n x=\frac{7\pi}{6}+2\pi n,\ \ \ x\ =\ \frac{11\pi}{6}+2\pi n x = 6 7 π + 2 π n , x = 6 1 1 π + 2 π n

x = π 6 + 2 π n , x = 5 π 6 + 2 π n x=\frac{\pi}{6}+2\pi n,\ \ \ x\ =\ \frac{5\pi}{6}+2\pi n x = 6 π + 2 π n , x = 6 5 π + 2 π n

x = 4 π 3 + 2 π n , x = 5 π 3 + 2 π n x=\frac{4\pi}{3}+2\pi n,\ \ \ \ x=\frac{5\pi}{3}+2\pi n x = 3 4 π + 2 π n , x = 3 5 π + 2 π n

x = π 4 + π n x=\frac{\pi}{4}+\pi n x = 4 π + π n

2 sin ⁡ x − 1 = 0 2\sin x-1=0 2 sin x − 1 = 0

x = π 6 + 2 π n , x = 5 π 6 + 2 π n x=\frac{\pi}{6}+2\pi n,\ \ \ \ x=\frac{5\pi}{6}+2\pi n x = 6 π + 2 π n , x = 6 5 π + 2 π n

x = π 3 + π n , x = 2 π 3 + π n x=\frac{\pi}{3}+\pi n,\ \ \ \ \ x\ =\ \frac{2\pi}{3}+\pi n x = 3 π + π n , x = 3 2 π + π n

x = π 6 + 2 π n , x = 7 π 6 + 2 π n x=\frac{\pi}{6}+2\pi n,\ \ \ \ \ x=\frac{7\pi}{6}+2\pi n x = 6 π + 2 π n , x = 6 7 π + 2 π n

S o l v e 4 cos ⁡ x + 3 = 5 f o r 0 ≤ x < 360 ° Solve\ \ \ 4\cos x+3=5\ \ \ for\ 0\le x<360\degree S o l v e 4 cos x + 3 = 5 f o r 0 ≤ x < 3 6 0 °

x = 60 ° , 300 ° x\ =\ 60\degree,\ 300\degree x = 6 0 ° , 3 0 0 °

x = 60 ° , 120 ° x\ =\ 60\degree,\ 120\degree x = 6 0 ° , 1 2 0 °

x = 30 ° , 150 ° x\ =\ 30\degree,\ 150\degree x = 3 0 ° , 1 5 0 °

x = 30 ° , 330 ° x\ =\ 30\degree,\ 330\degree x = 3 0 ° , 3 3 0 °

S o l v e 3 cot ⁡ x + 5 = 8 f o r 0 ≤ x < 2 π Solve\ 3\cot x\ +\ 5\ =\ 8\ \ for\ \ 0\ \le\ x\ <\ 2\pi S o l v e 3 cot x + 5 = 8 f o r 0 ≤ x < 2 π

π 4 , 5 π 4 \frac{\pi}{4},\ \frac{5\pi}{4} 4 π , 4 5 π

π 2 , 3 π 2 \frac{\pi}{2},\ \frac{3\pi}{2} 2 π , 2 3 π

3 π 4 , 7 π 4 \frac{3\pi}{4},\ \frac{7\pi}{4} 4 3 π , 4 7 π

Solve for x: cos ⁡ ( x ) = 3 2 \cos\left(x\right)=\frac{\sqrt{3}}{2} cos ( x ) = 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

− π 2 -\frac{π}{2} − 2 π

Solve for x: tan ⁡ ( x ) = − 3 \tan\left(x\right)\ =-\sqrt{3} tan ( x ) = − 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

− π 3 -\frac{π}{3} − 3 π

− π 2 -\frac{\pi}{2} − 2 π

Which is a correct way to solve the equation cosx(2cosx − 3) = 0?

set each factor equal to 0 and solve

distribute cosx into the parentheses

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

cos x is never equal to a fraction

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

This equation will have a solution tomorrow.

Choose a good way to start solving this equation tanx sin 2 x = 2 tanx

subtract 2 tanx from the left and then factor tanx out

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

π 4 , 3 π 4 , 5 π 4 a n d 7 π 4 \frac{π}{4},\frac{3π}{4},\frac{5π}{4}\ and\ \frac{7π}{4} 4 π , 4 3 π , 4 5 π a n d 4 7 π

3 π 4 a n d 5 π 4 \frac{3π}{4}and\ \frac{5π}{4}\ 4 3 π a n d 4 5 π

π 4 a n d 3 π 4 \frac{π}{4}and\ \frac{3π}{4} 4 π a n d 4 3 π

π 6 a n d 5 π 6 \frac{\pi}{6}\ and\ \frac{5\pi}{6} 6 π a n d 6 5 π

Solving Trig Basic Trig Equations

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MULTIPLE CHOICE QUESTION

2 mins • 2 pts

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

No solution

3π/2

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

3 mins • 2 pts

Solve on the domain [0, 2π)
4sin²x = 3

π/6, 11π/6

π/3, 2π/3

π/6, 5π/6, 7π/6, 11π/6

π/3, 2π/3, 4π/3, 5π/3

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

3 mins • 2 pts

Solve on the domain [0, 2π)
cos x + 2 = 3 cos x

0, 2π/3, 4π/3

No solution

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

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

No solution

3π/2

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Which of the following is NOT
a solution to
$\sin x=\frac{\sqrt{3}}{2}$ ?

$\frac{\pi}{3}$

$\frac{2\pi}{3}$

$\frac{7\pi}{3}$

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

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Solve $\sin x=-1$
on the interval $\left[0,2\pi\right)$

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

$x=\frac{\pi}{2}$

$x=\frac{3\pi}{2}$

$x=\pi$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

One solution of tan x = -1 is 135⁰, which of these is another solution?

315⁰

135⁰

225⁰

330⁰

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

What is a good first step to solving this equation?

$5\cos x-\sqrt{3}=3\cos x$

Divide everything by 5

Subtract $3\cos x$ from both sides of the equation

Divide everything by 3

Add $3\cos x$ to both sides of the equation

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

What is a good next step to solving this equation?

$2\cos x-\sqrt{3}=0$

Subtract $\sqrt{3}$ from both sides of the equation

Add $\sqrt{3}$ to both sides of the equation

Divide both sides of the equation by $\cos x$

Stop because there is no solution

10.

MULTIPLE SELECT QUESTION

2 mins • 1 pt

Check all solutions to this equation
$\cos x=\frac{\sqrt{3}}{2}$

$\frac{\pi}{6}+2n\pi$

$\frac{\pi}{3}+2n\pi$

$\frac{11\pi}{6}+2n\pi$

$\frac{2\pi}{3}+2n\pi$

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Solving Trig Basic Trig Equations

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

Solve on the domain [0, 2π)4sin2x = 3

Solve on the domain [0, 2π)cos x + 2 = 3 cos x

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

Which of the following is NOT a solution to sin⁡x=32\sin x=\frac{\sqrt{3}}{2}sinx=23​​ ?

Solve sin⁡x=−1\sin x=-1sinx=−1 on the interval [0,2π)\left[0,2\pi\right)[0,2π)

One solution of tan x = -1 is 135⁰, which of these is another solution?

What is a good first step to solving this equation? 5cos⁡x−3=3cos⁡x5\cos x-\sqrt{3}=3\cos x5cosx−3​=3cosx

What is a good next step to solving this equation? 2cos⁡x−3=02\cos x-\sqrt{3}=02cosx−3​=0

Check all solutions to this equation cos⁡x=32\cos x=\frac{\sqrt{3}}{2}cosx=23​​

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

Solve on the domain [0, 2π)
4sin²x = 3

Solve on the domain [0, 2π)
cos x + 2 = 3 cos x

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

Which of the following is NOT
a solution to
$\sin x=\frac{\sqrt{3}}{2}$ ?

Solve $\sin x=-1$
on the interval $\left[0,2\pi\right)$

What is a good first step to solving this equation?

$5\cos x-\sqrt{3}=3\cos x$

What is a good next step to solving this equation?

$2\cos x-\sqrt{3}=0$

Check all solutions to this equation
$\cos x=\frac{\sqrt{3}}{2}$