# Can someone explain this solution (1 Viewer)

#### Life'sHard

##### Well-Known Member
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
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
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

##### Active Member
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.

• Life'sHard

#### Hivaclibtibcharkwa

##### 𝗕𝗶𝗼𝗹𝗼𝗴𝘆 𝗧𝘂𝘁𝗼𝗿
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