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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.
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If cos and theta 0.65 what is the value of sin and theta?
You can use the Pythagorean identity to solve this:(sin theta) squared + (cos theta) squared = 1.
What is sec squared theta times cos squared theta minus tan squared theta?
Tan^2
What is sin squared equal to?
Sin squared is equal to 1 - cos squared.
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
What is cos 360 minus theta?
- cos theta
Sin squared theta plus cos squared theta barabar Kya Hota Hai?
1
What is cos theta times cos theta?
Cos theta squared
How do you prove cot squared theta plus cos squared theta plus sin squared theta scs squared theta?
Until an "equals" sign shows up somewhere in the expression, there's nothing to prove.
How do you solve cos theta subtract cos squared theta divide 1 plus cos theta?
The question contains an expression but not an equation. An expression cannot be solved.
How do you solve theta if cos squared theta equals 1 and 0 is less than or equal to theta which is less than 2pi?
cos2(theta) = 1 so cos(theta) = ±1 cos(theta) = -1 => theta = pi cos(theta) = 1 => theta = 0
If cos and theta 0.65 what is the value of sin and theta?
You can use the Pythagorean identity to solve this:(sin theta) squared + (cos theta) squared = 1.
What is sec squared theta times cos squared theta minus tan squared theta?
Tan^2
What is sin squared theta cos squared theta?
If there is a plus in between, that would be equal to 1, as a result of the Pythagorean Theorem. Otherwise, you can convert this into other forms with some of the trigonometric identities for multiplication, but you won't really get it into a simpler form.
Which basic trigonometric identity is actually a statement of the pythagorean theorem?
COS squared Theta + SIN squared Theta = 1; where Theta is the angles measurement in degrees.
What is cos theta minus cos theta times sin squared theta?
cos(t) - cos(t)*sin2(t) = cos(t)*[1 - sin2(t)] But [1 - sin2(t)] = cos2(t) So, the expression = cos(t)*cos2(t) = cos3(t)
How would you solve and show work for cos2 theta if cos squared theta equals 1 and theta is in the 4th quadrant?
cos2(theta) = 1 cos2(theta) + sin2(theta) = 1 so sin2(theta) = 0 cos(2*theta) = cos2(theta) - sin2(theta) = 1 - 0 = 1
Prove that sin theta power 8 - cos theta power 8 equal to sin sq Theta -cos sq x 1-sin sq Theta cos sq theta?
The equation cannot be proved because of the scattered parts.
