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sine^2 theta -4 + cos^2 theta equals what?

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2 Answers

     sin2θ - 4 + cos2θ

Notice that there is a trigonometric identity within this expression, that being the pythagorean trig identity which states that following:     sin2θ + cos2θ = 1

It follows from the pythagorean theorem that if the length of the hypotenuse of a right triangle is 1 then the lengths of the legs are the sine and cosine of one of the angles, which yields the above trig identity that always holds true.

Therefore,

     sin2θ - 4 + cos2θ     <==>     (sin2θ + cos2θ) - 4  =  1 - 4  =  -3

sin2(Θ)-4+cos2(Θ)=

we know ...  sin2(Θ)+cos2(Θ)=1

so sin2(Θ)+cos2(Θ) -4 = 1 - 4

so the answer is -3

Comments

So sin2(T)+cos2(T)=1 is an identity and,

something a student should simply memorize?

You should absolutely memorize this identity, you will use it for your entire mathematical career.