Question

Выразите тригонометрические функции угла a через sin a.

Answer 1

$cosa=б\sqrt{1-sin^2a} \\ \\ tga=\frac{sina}{cosa}=б\frac{sina}{\sqrt{1-sin^2a}} \\ \\ ctga=\frac{cosa}{sina}=б\frac{\sqrt{1-sin^2a}}{sina}$

Answer 2

Expressing Trigonometric Functions in Terms of sin(a)

To express the trigonometric functions of an angle *a* in terms of sin(*a*), we can use the following relationships:

1. cosine function (cos): - The cosine function can be expressed in terms of the sine function using the identity: cos(*a*) = ±√(1 - sin²(*a*)).

2. tangent function (tan): - The tangent function can be expressed in terms of the sine function using the identity: tan(*a*) = sin(*a*) / √(1 - sin²(*a*)).

3. cotangent function (cot): - The cotangent function can be expressed in terms of the sine function using the identity: cot(*a*) = 1 / tan(*a*) = √(1 - sin²(*a*)) / sin(*a*).

4. secant function (sec): - The secant function can be expressed in terms of the sine function using the identity: sec(*a*) = 1 / cos(*a*) = 1 / (±√(1 - sin²(*a*))).

5. cosecant function (csc): - The cosecant function can be expressed in terms of the sine function using the identity: csc(*a*) = 1 / sin(*a*).

These relationships allow us to express various trigonometric functions in terms of the sine function, providing a useful way to relate different trigonometric quantities to each other.

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