# Solve the Last Big Question on Degrees: Sin(45ds+x)+cos(45ds+x)=sqrt2cosx

• majinknight
In summary, the conversation is about a math problem involving the sine and cosine of a special angle. The person is struggling to solve it and needs help. The other person provides some hints and the person eventually figures it out. The conversation then shifts to the age and location of the person who asked for help. They are in Ontario, Canada and in 11th grade.
majinknight
Ok the last question on those pages of question is this and i have got stuck and can't figure it out. I need to show that (ds=degrees)
Sin(45ds+x) +cos(45ds+x) = sqaureroot2 cosx.
Ok so i did left side first and changed it to.
Sin45Cosy + Cos45Siny +Cos45Cosy - Sin45Siny
Now what i want to do is divide out the CosY and Sin Y but even if i do that it doesn't make square root two and i don't know what to do from there. Can you help me solve this last practise question.

They've given you a trig problem that includes the sine and cosine of
a special angle. That should prod you in the right direction. If not, look at the attached text file.

#### Attachments

• sincos.txt
275 bytes · Views: 238
What you are doing doesn't make a whole lot of sense. What is Y?

sin(45+ x)= sin(45)cos(x)+ cos(45)sin(x) and
cos(45+ x)= cos(45)cos(x)- sin(45)sin(x).

Do you know what sin(45) and cos(45) are?

Plug those into the two equations above and add.

Oh ok i get it, you i thought of putting the 1/root2 in but wasnt sure how to go from there but i understand now. Thankyou so much!

Originally posted by majinknight
Ok the last question on those pages of question is this and i have got stuck and can't figure it out. I need to show that (ds=degrees)
Sin(45ds+x) +cos(45ds+x) = sqaureroot2 cosx.
Ok so i did left side first and changed it to.
Sin45Cosy + Cos45Siny +Cos45Cosy - Sin45Siny
Now what i want to do is divide out the CosY and Sin Y but even if i do that it doesn't make square root two and i don't know what to do from there. Can you help me solve this last practise question.

how old are you buddy?

16 currently in grade 11. Why?

Originally posted by PrudensOptimus
how old are you buddy?

Haven't you discovered the "Profile" button yet, buddy? :)

Just testing out the "math typesetting" thing:

\begin{align*} \sin(45^\circ + x) &= \sin(45^\circ) \cos x + \cos(45^\circ) \sin x \\ &= \frac{\cos x}{\sqrt{2}} + \frac{\sin x}{\sqrt{2}} \\ &= \frac{\cos x + \sin x}{\sqrt{2}} \end{align*}

Originally posted by majinknight
16 currently in grade 11. Why?

lol which state are you in?

Im in Ontario Canada. Its a province not a state.

are you in the Canadian school system?

Yes i am, i am glad you are all so interested in me. I feel so special

heh, it sounded a lot like one of our A-level questions, i was curious about it.

## What is the last big question on degrees?

The last big question on degrees is how to solve the equation: Sin(45ds+x)+cos(45ds+x)=sqrt2cosx. This equation involves trigonometric functions and requires solving for the variable x.

## What are the steps to solve this equation?

The first step is to use the trigonometric identity: Sin(45ds+x)=sqrt2/2(cosx+sinx) to rewrite the equation as sqrt2/2(cosx+sinx)+cos(45ds+x)=sqrt2cosx. Then, simplify the equation by distributing the sqrt2/2 and combining like terms. Finally, solve for x by isolating the variable on one side of the equation.

## What are the possible solutions for x?

There are multiple possible solutions for x, as this equation has periodic solutions. In other words, the same values of x will satisfy the equation for different values of ds. Additionally, there may be multiple values of x that satisfy the equation for a given value of ds.

## What are the implications of solving this equation?

Solving this equation can have various implications depending on the context in which it is being used. In mathematics, it can help with understanding trigonometric identities and solving equations involving trigonometric functions. In other fields, such as physics or engineering, it may be useful in solving problems related to angles and rotations.

## Are there any real-world applications of this equation?

Yes, there are real-world applications of this equation. For example, in navigation, this equation can be used to calculate the angle between two objects or to determine the position of an object based on its angle and distance from a known point. It can also be used in fields such as astronomy, surveying, and architecture.

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