Solving Trigonometric Equations

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What is a trigonometric equation?

Back

A trigonometric equation is an equation that involves trigonometric functions of a variable, typically an angle. Examples include equations like sin(x) = 0.5 or cos(2x) = 1.

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CCSS.HSF.TF.B.7

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What are the primary trigonometric functions?

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The primary trigonometric functions are sine (sin), cosine (cos), and tangent (tan). They relate the angles of a triangle to the ratios of its sides.

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CCSS.HSF.TF.A.2

Front

What is the range of the sine function?

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The range of the sine function is from -1 to 1, meaning that for any angle x, -1 <= sin(x) <= 1.

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CCSS.HSF.TF.A.4

Front

What is the range of the cosine function?

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The range of the cosine function is also from -1 to 1, meaning that for any angle x, -1 <= cos(x) <= 1.

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CCSS.HSF-IF.C.7E

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What is the tangent function defined as?

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The tangent function is defined as the ratio of the sine and cosine functions: tan(x) = sin(x)/cos(x).

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CCSS.HSF.TF.A.2

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What is the unit circle?

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The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane. It is used to define trigonometric functions for all angles.

Tags

CCSS.HSF.TF.A.2

Front

How do you solve the equation sin(x) = 0.5?

Back

To solve sin(x) = 0.5, find the angles where sine equals 0.5. The solutions in the interval [0, 2π) are x = π/6 and x = 5π/6.

Tags

CCSS.HSF.TF.B.7

Front

What is the Pythagorean identity?

Back

The Pythagorean identity states that for any angle x, sin²(x) + cos²(x) = 1.

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CCSS.HSF.TF.C.8

Front

What are the solutions to the equation cos(x) = 0?

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The solutions to cos(x) = 0 in the interval [0, 2π) are x = π/2 and x = 3π/2.

Tags

CCSS.HSF.TF.B.7

Front

What is the inverse sine function?

Back

The inverse sine function, denoted as sin⁻¹ or arcsin, is used to find the angle whose sine is a given number. Its range is [-π/2, π/2].

Tags

CCSS.HSF.TF.B.7