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They are mathematical functions.

Most people are introduced to them as trigonometric functions. In the context of a right angled triangle, with one of its angles being theta,

Cos(theta) = The ratio of the lengths of the adjacent side and the hypotenuse.

Sin(theta) = The ratio of the lengths of the opposite side and the hypotenuse.

More advanced mathematicians will know them simply as the following infinite series:

Cos(theta) = 1 - x2/2! + x4/4! - x6/6! + ...

and

Sin(theta) = x/1! - x3/3! + x5/5! - x7/7! + ...

n! = 1*2*3* ... *n

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Q: What is cos theta and sin theta?

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Remember that tan = sin/cos. So your expression is sin/cos times cos. That's sin(theta).

It's 1/2 of sin(2 theta) .

Let 'theta' = A [as 'A' is easier to type] sec A - 1/(sec A) = 1/(cos A) - cos A = (1 - cos^2 A)/(cos A) = (sin^2 A)/(cos A) = (tan A)*(sin A) Then you can swap back the 'A' with theta

1 cot(theta)=cos(theta)/sin(theta) cos(45 degrees)=sqrt(2)/2 AND sin(45 degrees)=sqrt(2)/2 cot(45 deg)=cos(45 deg)/sin(deg)=(sqrt(2)/2)/(sqrt(2)/2)=1

tan θ = sin θ / cos θ sec θ = 1 / cos θ sin ² θ + cos² θ = 1 → sin² θ - 1 = - cos² θ → tan² θ - sec² θ = (sin θ / cos θ)² - (1 / cos θ)² = sin² θ / cos² θ - 1 / cos² θ = (sin² θ - 1) / cos² θ = - cos² θ / cos² θ = -1

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Remember that tan = sin/cos. So your expression is sin/cos times cos. That's sin(theta).

'csc' = 1/sin'tan' = sin/cosSo it must follow that(cos) (csc) / (tan) = (cos) (1/sin)/(sin/cos) = (cos) (1/sin) (cos/sin) = (cos/sin)2

(Sin theta + cos theta)^n= sin n theta + cos n theta

It's 1/2 of sin(2 theta) .

You can use the Pythagorean identity to solve this:(sin theta) squared + (cos theta) squared = 1.

because sin(2x) = 2sin(x)cos(x)

The fourth Across the quadrants sin theta and cos theta vary: sin theta: + + - - cos theta: + - - + So for sin theta < 0, it's the third or fourth quadrant And for cos theta > 0 , it's the first or fourth quadrant. So for sin theta < 0 and cos theta > 0 it's the fourth quadrant

The derivative of (sin (theta))^.5 is (cos(theta))/(2sin(theta))

sin/cos

The equation cannot be proved because of the scattered parts.

(/) = theta sin 2(/) = 2sin(/)cos(/)

Let 'theta' = A [as 'A' is easier to type] sec A - 1/(sec A) = 1/(cos A) - cos A = (1 - cos^2 A)/(cos A) = (sin^2 A)/(cos A) = (tan A)*(sin A) Then you can swap back the 'A' with theta

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