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To determine what negative sine squared plus cosine squared is equal to, start with the primary trigonometric identity, which is based on the pythagorean theorem...

sin2(theta) + cos2(theta) = 1

... and then solve for the question...


cos2(theta) = 1 - sin2(theta)

2 cos2(theta) = 1 - sin2(theta) + cos2(theta)

2 cos2(theta) - 1 = - sin2(theta) + cos2(theta)

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โˆ™ 2009-11-18 02:50:19
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Q: What does negative sine squared plus cosine squared equal?
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Continue Learning about Trigonometry

What is 1 plus cotangent squared?

1 + cot2x = csc2x


Why does sin theta squared plus cos theta squared equal 1?

Sin2(theta) + cos2(theta) = 1 for the same reason that the sides of a right triangle squared equal the hypotenuse squared - The pythagorean theorem.In the unit circle (origin = (0,0), radius = 1), an angle theta is the angle made by some arbitrary ray drawn from the origin at an angle relative to the x axis. The point of that ray that intersects with the circle is the point (x,y).Sin(theta) is defined as x, and cos(theta) is defined as y. These are primary trigonometric identities, which link trigonometry with geometry.Since the points (0,0) (x,0) (x,y) (0,x) describe a right triangle, with (0,x) (0,0) (x,0) being the right angle, then x2 + y2 = 12, or sin2(theta) + cos2(theta) = 1.If this is not clear, draw a circle around the origin, draw a line from the center to an arbitrary point on the circle, and draw the x and y perpendiculars of that point to each axis. You will see a right triangle. X is sine, Y is cosine, and 1 is hypotenuse. It does not matter if X and/or Y is negative - the squaring will make it positive - and the pythagorean theorem should be visible.


What is this expression as the cosine of an angle cos30cos55 plus sin30sin55?

cos(30)cos(55)+sin(30)sin(55)=cos(30-55) = cos(-25)=cos(25) Note: cos(a)=cos(-a) for any angle 'a'. cos(a)cos(b)+sin(a)sin(b)=cos(a-b) for any 'a' and 'b'.


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If a cos theta plus b sin theta equals 8 and a sin theta - b cos theta equals 5 show that a squared plus b squared equals 89?

There is a hint to how to solve this in what is required to be shown: a and b are both squared.Ifa cos θ + b sin θ = 8a sin θ - b cos θ = 5then square both sides of each to get:a² cos² θ + 2ab cos θ sin θ + b² sin² θ = 64a² sin² θ - 2ab sin θ cos θ + b² cos² θ = 25Now add the two together:a² cos² θ + a² sin² θ + b² sin² θ + b² cos² θ = 89→ a²(cos² θ + sin² θ) + b² (sin² θ + cos² θ) = 89using cos² θ + sin² θ = 1→ a² + b² = 89

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