Basic Trigonometry Formulas

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What is the definition of the sine function in a right triangle?
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Sine of an angle is equal to the opposite side divided by the hypotenuse.
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What is the definition of the cosine function in a right triangle?
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Cosine of an angle is equal to the adjacent side divided by the hypotenuse.
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What is the definition of the tangent function in a right triangle?
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Tangent of an angle is equal to the opposite side divided by the adjacent side.
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What is the Pythagorean identity in trigonometry?
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The Pythagorean identity is sin²θ + cos²θ = 1.
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What is the formula for tangent in terms of sine and cosine?
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tanθ = sinθ/cosθ.
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How do you express sine in terms of cosine?
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sinθ = √(1 - cos²θ).
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How do you express cosine in terms of sine?
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cosθ = √(1 - sin²θ).
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What is the formula for secant in terms of cosine?
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secθ = 1/cosθ.
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What is the formula for cosecant in terms of sine?
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cscθ = 1/sinθ.
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What is the formula for cotangent in terms of tangent?
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cotθ = 1/tanθ.
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How do you express cotangent in terms of sine and cosine?
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cotθ = cosθ/sinθ.
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What is the co-function identity relating sine and cosine?
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sin(90° - θ) = cosθ and cos(90° - θ) = sinθ.
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What is the angle sum identity for sine?
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sin(α + β) = sinα cosβ + cosα sinβ.
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What is the angle sum identity for cosine?
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cos(α + β) = cosα cosβ - sinα sinβ.
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What is the angle sum identity for tangent?
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tan(α + β) = (tanα + tanβ) / (1 - tanαtanβ).
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