Solve cos ⁡ θ = − 0.23 \cos\theta=-0.23\ cos θ = − 0 . 2 3 for 0 ° ≤ θ ≤ 360 ° 0\degree\le\theta\le360\degree 0 ° ≤ θ ≤ 3 6 0 ° giving answers to 1 decimal place

θ = 103.3 ° , 256.7 ° \theta=103.3\degree,256.7\degree θ = 1 0 3 . 3 ° , 2 5 6 . 7 °

θ = 76.6 ° , 103.3 ° \theta=76.6\degree,103.3\degree θ = 7 6 . 6 ° , 1 0 3 . 3 °

θ = 76.7 ° , 283.3 ° \theta=76.7\degree,283.3\degree θ = 7 6 . 7 ° , 2 8 3 . 3 °

θ = 103.3 ° , 283.3 ° \theta=103.3\degree,283.3\degree θ = 1 0 3 . 3 ° , 2 8 3 . 3 °

Solve tan ⁡ θ = 1.4 \tan\theta=1.4 tan θ = 1 . 4 for 0 ° ≤ θ ≤ 360 ° 0\degree\le\theta\le360\degree 0 ° ≤ θ ≤ 3 6 0 ° giving your answer to one decimal place.

θ = 54.5 ° , 234.5 ° \theta=54.5\degree,234.5\degree θ = 5 4 . 5 ° , 2 3 4 . 5 °

θ = 54.5 ° , 125.5 ° \theta=54.5\degree,\ 125.5\degree θ = 5 4 . 5 ° , 1 2 5 . 5 °

θ = 125.5 ° , 305.5 ° \theta=125.5\degree,305.5\degree θ = 1 2 5 . 5 ° , 3 0 5 . 5 °

θ = 234.5 ° , 305.5 ° \theta=234.5\degree,305.5\degree θ = 2 3 4 . 5 ° , 3 0 5 . 5 °

Solve sin ⁡ θ = − 0.32 \sin\theta=-0.32 sin θ = − 0 . 3 2 for 0 ≤ θ ≤ 2 π 0\le\theta\le2\pi 0 ≤ θ ≤ 2 π giving your answers to 3 significant figures

θ = 3.47 , 5.96 \theta=3.47,5.96 θ = 3 . 4 7 , 5 . 9 6

θ = 0.325 , 3.47 \theta=0.325,3.47 θ = 0 . 3 2 5 , 3 . 4 7

θ = 2.81 , 5.96 \theta=2.81,\ 5.96 θ = 2 . 8 1 , 5 . 9 6

θ = 2.81 , 3.47 \theta=2.81,3.47 θ = 2 . 8 1 , 3 . 4 7

Solve 3 cos ⁡ θ − 2 sin ⁡ θ cos ⁡ θ = 0 \sqrt{3}\cos\theta-2\sin\theta\cos\theta=0 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"> cos θ − 2 sin θ cos θ = 0 for 0 ≤ θ ≤ 2 π 0\le\theta\le2\pi 0 ≤ θ ≤ 2 π

θ = π 2 , 3 π 2 , π 3 , 2 π 3 \theta=\frac{\pi}{2},\frac{3\pi}{2},\frac{\pi}{3},\frac{2\pi}{3} θ = 2 π , 2 3 π , 3 π , 3 2 π

θ = π 3 , 2 π 3 \theta=\frac{\pi}{3},\frac{2\pi}{3} θ = 3 π , 3 2 π

θ = π 2 , 3 π 2 \theta=\frac{\pi}{2},\frac{3\pi}{2} θ = 2 π , 2 3 π

θ = π 2 , 3 π 2 , π 6 , 5 π 6 \theta=\frac{\pi}{2},\frac{3\pi}{2},\frac{\pi}{6},\frac{5\pi}{6} θ = 2 π , 2 3 π , 6 π , 6 5 π

Solve tan ⁡ θ 2 = 2.1 \tan\ \frac{\theta}{2}=2.1 tan 2 θ = 2 . 1 for 0 ≤ θ ≤ 2 π 0\le\theta\le2\pi 0 ≤ θ ≤ 2 π giving your answers to 3 significant figures

θ = 2.25 \theta=2.25 θ = 2 . 2 5

θ = 2.25 , 4.27 \theta=2.25,4.27 θ = 2 . 2 5 , 4 . 2 7

θ = 0.563 , 2.13 \theta=0.563,2.13 θ = 0 . 5 6 3 , 2 . 1 3

θ = 0.563 \theta=0.563 θ = 0 . 5 6 3

Find the general solution of the equation 2 sin ⁡ 3 θ = 3 2\sin3\theta=\sqrt{3} 2 sin 3 θ = 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">

θ = ( − 1 ) n π 9 + n π 3 , n ∈ Z \theta=\left(-1\right)^n\ \frac{\pi}{9}+\frac{n\pi}{3}\ \ ,\ \ n\in Z θ = ( − 1 ) n 9 π + 3 n π , n ∈ Z

θ = ( − 1 ) n π 18 + n π 3 , n ∈ Z \theta=\left(-1\right)^n\ \ \frac{\pi}{18\ }+\frac{n\pi}{3}\ \ ,\ n\in Z θ = ( − 1 ) n 1 8 π + 3 n π , n ∈ Z

θ = ( − 1 ) n π 9 + n π , n ∈ Z \theta=\left(-1\right)^n\ \ \frac{\pi}{9}+n\pi\ \ ,\ \ n\in Z θ = ( − 1 ) n 9 π + n π , n ∈ Z

θ = ( − 1 ) n π + 3 n π , n ∈ Z \theta=\left(-1\right)^n\ \pi+3n\pi\ \ ,\ n\in Z θ = ( − 1 ) n π + 3 n π , n ∈ Z

Find the general solution of the equation tan ⁡ 2 θ = − 1 \tan2\theta=-1 tan 2 θ = − 1

θ = − π 8 + n π 2 , n ∈ Z \theta=-\frac{\pi}{8}+\frac{n\pi}{2}\ \ ,\ \ n\in Z θ = − 8 π + 2 n π , n ∈ Z

θ = π 8 + n π , n ∈ Z \theta=\frac{\pi}{8}+n\pi\ \ ,\ n\in Z θ = 8 π + n π , n ∈ Z

θ = − π 8 + n π , n ∈ Z \theta=-\frac{\pi}{8}+n\pi\ \ ,\ \ n\in Z θ = − 8 π + n π , n ∈ Z

θ = π 8 + n π 2 , n ∈ Z \theta=\frac{\pi}{8}+\frac{n\pi}{2}\ \ ,\ n\in Z θ = 8 π + 2 n π , n ∈ Z

Find the general solution of cos ⁡ ( θ − 10 ° ) = 1 \cos\left(\theta-10\degree\right)=1 cos ( θ − 1 0 ° ) = 1

θ = 360 ° n + 10 ° , n ∈ Z \theta=360\degree n+10\degree\ \ ,\ n\in Z θ = 3 6 0 ° n + 1 0 ° , n ∈ Z

θ = 2 n π − 10 , n ∈ Z \theta=2n\pi-10\ \ ,\ \ n\in Z θ = 2 n π − 1 0 , n ∈ Z

θ = 2 n π + 10 , n ∈ Z \theta=2n\pi+10\ \ ,\ n\in Z θ = 2 n π + 1 0 , n ∈ Z

θ = 360 ° n − 10 ° , n ∈ Z \theta=360\degree n-10\degree\ \ ,\ n\in Z θ = 3 6 0 ° n − 1 0 ° , n ∈ Z

Find the values of R and θ \theta θ for which 12 cos ⁡ θ + 35 sin ⁡ θ ≡ R cos ⁡ ( θ − α ) 12\cos\theta+35\sin\theta\equiv R\cos\left(\theta-\alpha\right) 1 2 cos θ + 3 5 sin θ ≡ R cos ( θ − α )

R = 37 , α = 1.24 r a d R=37\ \ ,\ \ \alpha=1.24\ rad R = 3 7 , α = 1 . 2 4 r a d

R = 37 , ∝ = 0.330 r a d R=37\ \ ,\ \ \propto=0.330\ rad R = 3 7 , ∝ = 0 . 3 3 0 r a d

R = 47 , α = 1.24 r a d R=47\ \ \ ,\ \ \alpha=1.24\ rad R = 4 7 , α = 1 . 2 4 r a d

R = 47 , α = 0.330 r a d R=47\ ,\ \ \alpha=0.330\ rad R = 4 7 , α = 0 . 3 3 0 r a d

Trigonometric Equations

Authored by Camille Tull

Mathematics

10th - 12th Grade

CCSS covered

Used 26+ times

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10 questions

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MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve $\cos\theta=-0.23\$ for $0\degree\le\theta\le360\degree$ giving answers to 1 decimal place

$\theta=76.6\degree,103.3\degree$

$\theta=103.3\degree,256.7\degree$

$\theta=76.7\degree,283.3\degree$

$\theta=103.3\degree,283.3\degree$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve $\tan\theta=1.4$ for $0\degree\le\theta\le360\degree$ giving your answer to one decimal place.

$\theta=54.5\degree,\ 125.5\degree$

$\theta=125.5\degree,305.5\degree$

$\theta=54.5\degree,234.5\degree$

$\theta=234.5\degree,305.5\degree$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve $\sin\theta=-0.32$ for $0\le\theta\le2\pi$ giving your answers to 3 significant figures

$\theta=0.325,3.47$

$\theta=3.47,5.96$

$\theta=2.81,\ 5.96$

$\theta=2.81,3.47$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve $\sqrt{3}\cos\theta-2\sin\theta\cos\theta=0$ for $0\le\theta\le2\pi$

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

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

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

$\theta=\frac{\pi}{2},\frac{3\pi}{2},\frac{\pi}{6},\frac{5\pi}{6}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve $8\sin^2\theta+2\sin\theta-3=0$
for $0\degree\le\theta\le360\degree$ giving your answers to the nearest degree

$\theta=49\degree,131\degree,229\degree,311\degree$

$\theta=30\degree,150\degree,49\degree,131\degree$

$\theta=49\degree,131\degree,210\degree,330\degree$

$\theta=30\degree,150\degree,229\degree,311\degree$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve $\tan\ \frac{\theta}{2}=2.1$ for $0\le\theta\le2\pi$ giving your answers to 3 significant figures

$\theta=2.25$

$\theta=2.25,4.27$

$\theta=0.563,2.13$

$\theta=0.563$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Find the general solution of the equation
$2\sin3\theta=\sqrt{3}$

$\theta=\left(-1\right)^n\ \frac{\pi}{9}+\frac{n\pi}{3}\ \ ,\ \ n\in Z$

$\theta=\left(-1\right)^n\ \ \frac{\pi}{18\ }+\frac{n\pi}{3}\ \ ,\ n\in Z$

$\theta=\left(-1\right)^n\ \ \frac{\pi}{9}+n\pi\ \ ,\ \ n\in Z$

$\theta=\left(-1\right)^n\ \pi+3n\pi\ \ ,\ n\in Z$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Find the general solution of the equation $\tan2\theta=-1$

$\theta=\frac{\pi}{8}+n\pi\ \ ,\ n\in Z$

$\theta=-\frac{\pi}{8}+\frac{n\pi}{2}\ \ ,\ \ n\in Z$

$\theta=-\frac{\pi}{8}+n\pi\ \ ,\ \ n\in Z$

$\theta=\frac{\pi}{8}+\frac{n\pi}{2}\ \ ,\ n\in Z$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Find the general solution of $\cos\left(\theta-10\degree\right)=1$

$\theta=2n\pi-10\ \ ,\ \ n\in Z$

$\theta=2n\pi+10\ \ ,\ n\in Z$

$\theta=360\degree n-10\degree\ \ ,\ n\in Z$

$\theta=360\degree n+10\degree\ \ ,\ n\in Z$

Tags

CCSS.HSF.TF.B.7

10.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Find the values of R and $\theta$ for which $12\cos\theta+35\sin\theta\equiv R\cos\left(\theta-\alpha\right)$

$R=37\ \ ,\ \ \alpha=1.24\ rad$

$R=37\ \ ,\ \ \propto=0.330\ rad$

$R=47\ \ \ ,\ \ \alpha=1.24\ rad$

$R=47\ ,\ \ \alpha=0.330\ rad$

Tags

CCSS.HSF.TF.C.9

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Trigonometric Equations

Solve cos⁡θ=−0.23 \cos\theta=-0.23\ cosθ=−0.23 for 0°≤θ≤360°0\degree\le\theta\le360\degree0°≤θ≤360° giving answers to 1 decimal place

Solve tan⁡θ=1.4\tan\theta=1.4tanθ=1.4 for 0°≤θ≤360°0\degree\le\theta\le360\degree0°≤θ≤360° giving your answer to one decimal place.

Solve sin⁡θ=−0.32\sin\theta=-0.32sinθ=−0.32 for 0≤θ≤2π0\le\theta\le2\pi0≤θ≤2π giving your answers to 3 significant figures

Solve 3cos⁡θ−2sin⁡θcos⁡θ=0\sqrt{3}\cos\theta-2\sin\theta\cos\theta=03​cosθ−2sinθcosθ=0 for 0≤θ≤2π0\le\theta\le2\pi0≤θ≤2π

Solve 8sin⁡2θ+2sin⁡θ−3=08\sin^2\theta+2\sin\theta-3=08sin2θ+2sinθ−3=0 for 0°≤θ≤360°0\degree\le\theta\le360\degree0°≤θ≤360° giving your answers to the nearest degree

Solve tan⁡ θ2=2.1\tan\ \frac{\theta}{2}=2.1tan 2θ​=2.1 for 0≤θ≤2π0\le\theta\le2\pi0≤θ≤2π giving your answers to 3 significant figures

Find the general solution of the equation 2sin⁡3θ=32\sin3\theta=\sqrt{3}2sin3θ=3​

Find the general solution of the equation tan⁡2θ=−1\tan2\theta=-1tan2θ=−1

Find the general solution of cos⁡(θ−10°)=1\cos\left(\theta-10\degree\right)=1cos(θ−10°)=1

Find the values of R and θ\thetaθ for which 12cos⁡θ+35sin⁡θ≡Rcos⁡(θ−α)12\cos\theta+35\sin\theta\equiv R\cos\left(\theta-\alpha\right)12cosθ+35sinθ≡Rcos(θ−α)

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Discover more resources for Mathematics

Solve $\cos\theta=-0.23\$ for $0\degree\le\theta\le360\degree$ giving answers to 1 decimal place

Solve $\tan\theta=1.4$ for $0\degree\le\theta\le360\degree$ giving your answer to one decimal place.

Solve $\sin\theta=-0.32$ for $0\le\theta\le2\pi$ giving your answers to 3 significant figures

Solve $\sqrt{3}\cos\theta-2\sin\theta\cos\theta=0$ for $0\le\theta\le2\pi$

Solve $8\sin^2\theta+2\sin\theta-3=0$
for $0\degree\le\theta\le360\degree$ giving your answers to the nearest degree

Solve $\tan\ \frac{\theta}{2}=2.1$ for $0\le\theta\le2\pi$ giving your answers to 3 significant figures

Find the general solution of the equation
$2\sin3\theta=\sqrt{3}$

Find the general solution of the equation $\tan2\theta=-1$

Find the general solution of $\cos\left(\theta-10\degree\right)=1$

Find the values of R and $\theta$ for which $12\cos\theta+35\sin\theta\equiv R\cos\left(\theta-\alpha\right)$