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3 years ago

13

Solve tan 10 - tan 50 +tan 70 with trigonometry.

1 answer:

Jobisdone [24]3 years ago

7 0

Below is the solution, I hope it helps.

<span>i) tan(70) - tan(50) = tan(60 + 10) - tan(60 - 10)

= {tan(60) + tan(10)}/{1 - tan(60)*tan(10)} - {tan(60) - tan(10)}/{1 + tan(10)*tan(60)}

ii) Taking LCM & simplifying with applying tan(60) = √3, the above simplifies to:

= 8*tan(10)/{1 - 3*tan²(10)}

iii) So tan(70) - tan(50) + tan(10) = 8*tan(10)/{1 - 3*tan²(10)} + tan(10)

= [8*tan(10) + tan(10) - 3*tan³(10)]/{1 - 3*tan²(10)}

= [9*tan(10) - 3*tan³(10)]/{1 - 3*tan²(10)}

= 3 [3*tan(10) - tan³(10)]/{1 - 3*tan²(10)}

= 3*tan(30) = 3*(1/√3) = √3 [Proved]

[Since tan(3A) = {3*tan(A) - tan³(A)}/{1 - 3*tan²(A)},
{3*tan(10) - tan³(10)}/{1 - 3*tan²(10)} = tan(3*10) = tan(30)]</span>

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3 years ago

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Convert the Cartesian equation (x 2 + y 2)2 = 4(x 2 - y 2) to a polar equation.

SashulF [63]

<u>ANSWER</u>

${r}^{2} = 4 \cos2\theta$

<u>EXPLANATION</u>

The Cartesian equation is

${( {x}^{2} + {y}^{2} )}^{2} = 4( {x}^{2} - {y}^{2} )$

We substitute

$x = r \cos( \theta)$

$y = r \sin( \theta)$

and

${x}^{2} + {y}^{2} = {r}^{2}$

This implies that

${( {r}^{2} )}^{2} = 4(( { r \cos\theta) }^{2} - {(r \sin\theta) }^{2} )$

Let us evaluate the exponents to get:

${r}^{4} = 4({ {r}^{2} \cos^{2}\theta } - {r}^{2} \sin^{2}\theta)$

Factor the RHS to get:

${r}^{4} = 4{r}^{2} ({ \cos^{2}\theta } - \sin^{2}\theta)$

Divide through by r²

${r}^{2} = 4 ({ \cos^{2}\theta } - \sin^{2}\theta)$

Apply the double angle identity

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3 years ago

Kellen bought new fish for her home aquarium. She bought 4 turquoise guppies and 3 sunburst tetra GLO fish and spent a total of

FromTheMoon [43]

Answer: A single turquoise guppy costs $3.69

Step-by-step explanation:

Let us use "x" to represent the amount a single turquoise is sold and use "y" to represent that of the Glo fish.

Since Kellen bought 4 guppies and 3 glo fishes for $41.73:

4x + 3y = 41.73 --------eqn 1

Similarly, Danielle purchased 3 guppies and 5 Glo fish for $56.02:

Therefore 3x + 5y = $56.02 -----eqn2

The 2 equations are;

4x + 3y = 41.73 (eqn 1)

3x + 5y = 56.02 (eqn 2)

We then solve the simultaneous equations using substitution method:

From eqn 1,

4x + 3y = 41.73

4x = 41.73 - 3y

x = (41.73 - 3y)/4

Substitute x for (41.73 - 3y)/4 in eqn2.

3[(41.73 - 3y)/4 + 5y = 56.02

11y + 125.19 = 224.08

11y =98.89

y = 98.89/11

y = $8.99

So, 1 Glo fish costs $8.99

Then, substitute "y" for 8.99 in equation 1

4x + (3×8.99) = 41.73

4x + 26.97 = 41.73

4x = 41.73 - 26.97

4x = 14.76

x = 14.76/4

x = $3.69

Therefore 1 turquoise guppy costs $3.69

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3 years ago

$82;35% discount answer

Musya8 [376]

82 times 0.35
the answer is 28.7

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