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Can someone explain this solution (1 Viewer)

Life'sHard

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Can you show the actual question which they’re asking you to find?

Well from what I’m reading they want you to find tan(theta)

So,
Standard sum of angle expansion in the first line then equate it. Then do the same with cos.

Then they simultaneous the 2 previous lines so that the sin cancels out and they are left with cos.

Then they solve for sin from the result of cos.

Then sin/cos=tan

Edit: If you’re confused about the working. Note that it’s only a “hint” so I suppose you could solve it differently.
 

Hivaclibtibcharkwa

𝗕𝗶𝗼𝗹𝗼𝗴𝘆 𝗧𝘂𝘁𝗼𝗿
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Can you show the actual question which they’re asking you to find?

Well from what I’m reading they want you to find tan(theta)

So,
Standard sum of angle expansion in the first line then equate it. Then do the same with cos.

Then they simultaneous the 2 previous lines so that the sin cancels out and they are left with cos.

Then they solve for sin from the result of cos.

Then sin/cos=tan

Edit: If you’re confused about the working. Note that it’s only a “hint” so I suppose you could solve it differently.
Oh they want us to find all 3 trig functions being sin,cos tan. I finally figured it out, it involved finding 2 equations and subbing them into each other
 

Hivaclibtibcharkwa

𝗕𝗶𝗼𝗹𝗼𝗴𝘆 𝗧𝘂𝘁𝗼𝗿
Joined
Jan 17, 2021
Messages
1,539
Gender
Male
HSC
2021
Can you show the actual question which they’re asking you to find?

Well from what I’m reading they want you to find tan(theta)

So,
Standard sum of angle expansion in the first line then equate it. Then do the same with cos.

Then they simultaneous the 2 previous lines so that the sin cancels out and they are left with cos.

Then they solve for sin from the result of cos.

Then sin/cos=tan

Edit: If you’re confused about the working. Note that it’s only a “hint” so I suppose you could solve it differently.
What’s another way to solve it
 

cossine

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What’s another way to solve it
So

sin(30 + theta) = something

=> sin^-1(sin(30+theta)) = sin^-1( something)

30+ theta = sin^-1( something)

theta = sin^-1( something) - 30.

Use this to find sin(theta).

I think they want exact value in this scenario though it is not specified in the question.
 

Hivaclibtibcharkwa

𝗕𝗶𝗼𝗹𝗼𝗴𝘆 𝗧𝘂𝘁𝗼𝗿
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So

sin(30 + theta) = something

=> sin^-1(sin(30+theta)) = sin^-1( something)

30+ theta = sin^-1( something)

theta = sin^-1( something) - 30.

Use this to find sin(theta).

I think they want exact value in this scenario though it is not specified in the question.
Yes they want exact value
 

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