SOLUTION: Please help me answer this question: Simplify sin ( - θ) sin (90θ + θ) - cos (180 θ

SOLUTION: Please help me answer this question: Simplify sin ( - θ) sin (90θ + θ) - cos (180 θ - θ) cos (270 θ +θ).

Question 1158099: Please help me answer this question:
Simplify
sin ( - θ) sin (90θ + θ) - cos (180 θ - θ) cos (270 θ +θ).
Answer by KMST(5377) (Show Source): You can put this solution on YOUR website!
I believe there was a mistake copying the formula in the question.
As written in the question, it says
,
which could be written more simply as
I do not know of a way to further simplify that, and it does not sound like a typical high school math question.

I suspect that the expression to simplify was meant to be

That could be simplified using the relations know between the trigonometric functions sine and cosine of angles that are reflected or turned by and .
You could find those relations in any list of "trigonometric identities",
but no need to memorize them, because you can visualize them for any angle in the unit circle.

For example, if we change the sign of the angle , sine changes sign, but cosine stays the same:
, but

Adding to an angle is turning it 1/4 of a circle, and turns sine into cosine and cosine into -sine.

So, and .

Using the two highlighted relations above we can start simplifying:

}

Also, adding to an angle (turning it half a circle), causes the sign to change for the sine and cosine functions.
So,
, but we know that , so
Similarly
, but we know that ,so

Using the highlighted relations above we can continue simplifying:

}

RELATED QUESTIONS
Simplify: cos 240 degrees. sin 15 degrees OVER (this is a fraction) cos(-30). cos 105... (answered by lwsshak3)

By considering a unit circle, decide whether the following are true or false: Sin 10<... (answered by Edwin McCravy)

sin 270 degrees+ cos (-180) degrees (answered by ikleyn)

please help me solve my homework: simplify: sin(90degrees+ x) sin ( 180 degrees +x) + cos (answered by stanbon)

Please help me solve this two part question: Given cos alpha= -4/5, 90 < alpha < 180... (answered by jim_thompson5910)

Evaluate sin 0 degrees+cos 180 degrees-sin 270... (answered by stanbon,solver91311)

Please help me solve this equation: If cos(a)=8/17 and 270� < a < 360�, then sin(a)... (answered by lwsshak3)

hi can you help me simplify this question. square root 3 cos x - sin (x + 60) - sin... (answered by lwsshak3)

Please help me solve this expression: sin 18 cos 12 + cos 18 sin... (answered by Fombitz)