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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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How do you simplify tan theta cos theta?
Remember that tan = sin/cos. So your expression is sin/cos times cos. That's sin(theta).
What is sin theta cos theta?
It's 1/2 of sin(2 theta) .
What is sec theta - 1 over sec 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
What is the cot of a 45 degree angle?
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
What is tan squared theta minus sec squared theta simplified?
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
