Solve, for $0 heta < 360^ ext{o}$, the equation 9sin(θ + 60°) = 4 giving your answers to 1 decimal place. You must show each step of your working. Solve, for $- ext{π} < x < ext{π}$, the equation 2tan x − 3sin x = 0 giving your answers to 2 decimal places where appropriate. [Solutions based entirely on graphical or numerical methods are not acceptable.]

A-Level Edexcel Maths Pure Solving Equations: Solve, for $0 heta

Solve, for $0 heta < 360^ ext{o}$, the equation 9sin(θ + 60°) = 4 giving your answers to 1 decimal place - Edexcel - A-Level Maths Pure - Question 8 - 2014 - Paper 1

Question 8

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Solve, for $0 heta < 360^ ext{o}$, the equation 9sin(θ + 60°) = 4 giving your answers to 1 decimal place. You must show each step of your working. Solve, for $- e... show full transcript

Worked Solution & Example Answer:Solve, for $0 heta < 360^ ext{o}$, the equation 9sin(θ + 60°) = 4 giving your answers to 1 decimal place - Edexcel - A-Level Maths Pure - Question 8 - 2014 - Paper 1

Step 1

Solve, for $0 heta < 360^ ext{o}$, the equation 9sin(θ + 60°) = 4

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Answer

To solve the equation, we start with:

$9 ext{sin}( heta + 60^ ext{o}) = 4$

Dividing both sides by 9: $ext{sin}( heta + 60^ ext{o}) = rac{4}{9}$

Next, we find the angle whose sine is $rac{4}{9}$ :

$heta + 60^ ext{o} = ext{sin}^{-1}igg( rac{4}{9}igg)\ heta + 60^ ext{o} ext{ is approximately } 26.3877^ ext{o}$

To find other angles within the range, we can also use: $heta + 60^ ext{o} = 180^ ext{o} - ext{sin}^{-1}igg( rac{4}{9}igg)\ heta + 60^ ext{o} = 180^ ext{o} - 26.3877^ ext{o}$

Calculating this gives: $heta + 60^ ext{o} ext{ is approximately } 153.6123^ ext{o}$

Subtracting 60° from both results:

ightarrow heta ext{ is approximately } -33.6123^ ext{o} ext{ (not within range)} $2.$ heta = 153.6123^ ext{o} - 60^ ext{o} ightarrow heta ext{ is approximately } 93.6123^ ext{o}$$

Now continuing with the other case: $heta + 60^ ext{o} = 360^ ext{o} - 26.3877^ ext{o} \ heta + 60^ ext{o} = 333.6123^ ext{o}$ Subtracting 60° again:

ightarrow heta ext{ is approximately } 273.6123^ ext{o} \ heta = 273.6^ ext{o} \ ext{(not within } 0 < heta < 360)$$ Thus, the answers in the correct range are: $$ heta ext{ approximately } 93.6^ ext{o} ext{ and } 326.4^ ext{o}$$

Step 2

Solve, for $- ext{π} < x < ext{π}$, the equation 2tan x − 3sin x = 0

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Answer

Starting with the equation:

$2 ext{tan}x - 3 ext{sin}x = 0$

This can be rearranged as: $2 ext{tan}x = 3 ext{sin}x$

Recalling that $ext{tan}x = rac{ ext{sin}x}{ ext{cos}x}$ , we substitute: $2 rac{ ext{sin}x}{ ext{cos}x} = 3 ext{sin}x$

Dividing both sides by $ext{sin}x$ (assuming $ext{sin}x eq 0$ ): $rac{2}{ ext{cos}x} = 3$

This simplifies to: $ext{cos}x = rac{2}{3}$

Now taking the inverse cosine: $x = ext{cos}^{-1}igg( rac{2}{3}igg)\ x ext{ is approximately } 0.8411$

The second solution in the range $- ext{π} < x < ext{π}$ can be found using: $x = - ext{cos}^{-1}igg( rac{2}{3}igg)\ x ext{ is approximately } -0.8411$

Thus the solutions are: $x ext{ approximately } 0.84 ext{ and } -0.84$

Solve, for $0 heta < 360^ ext{o}$, the equation 9sin(θ + 60°) = 4 giving your answers to 1 decimal place - Edexcel - A-Level Maths Pure - Question 8 - 2014 - Paper 1

Worked Solution & Example Answer:Solve, for $0 heta < 360^ ext{o}$, the equation 9sin(θ + 60°) = 4 giving your answers to 1 decimal place - Edexcel - A-Level Maths Pure - Question 8 - 2014 - Paper 1

Solve, for $0 heta < 360^ ext{o}$, the equation 9sin(θ + 60°) = 4

Solve, for $- ext{π} < x < ext{π}$, the equation 2tan x − 3sin x = 0

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