Basic Trigonometry Formulas

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What is the definition of the sine function in a right triangle?

Sine of an angle is equal to the opposite side divided by the hypotenuse.

What is the definition of the cosine function in a right triangle?

Cosine of an angle is equal to the adjacent side divided by the hypotenuse.

What is the definition of the tangent function in a right triangle?

Tangent of an angle is equal to the opposite side divided by the adjacent side.

What is the Pythagorean identity in trigonometry?

The Pythagorean identity is sin²θ + cos²θ = 1.

What is the formula for tangent in terms of sine and cosine?

tanθ = sinθ/cosθ.

How do you express sine in terms of cosine?

sinθ = √(1 - cos²θ).

How do you express cosine in terms of sine?

cosθ = √(1 - sin²θ).

What is the formula for secant in terms of cosine?

secθ = 1/cosθ.

What is the formula for cosecant in terms of sine?

cscθ = 1/sinθ.

What is the formula for cotangent in terms of tangent?

cotθ = 1/tanθ.

How do you express cotangent in terms of sine and cosine?

cotθ = cosθ/sinθ.

What is the co-function identity relating sine and cosine?

sin(90° - θ) = cosθ and cos(90° - θ) = sinθ.

What is the angle sum identity for sine?

sin(α + β) = sinα cosβ + cosα sinβ.

What is the angle sum identity for cosine?

cos(α + β) = cosα cosβ - sinα sinβ.

What is the angle sum identity for tangent?

tan(α + β) = (tanα + tanβ) / (1 - tanαtanβ).