Introduction to Trigonometry

10 Pages

English

High School

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Trigonometric Foundations

1. Measuring Angles in Degrees

2. Radians and Degree Conversion

3. Right Triangles and Trigonometric Ratios

4. Solving Right Triangles with Trigonometry

5. The Pythagorean Theorem and Special Triangles

Trigonometric Functions and Applications

6. The Unit Circle Connects Angles and Coordinates

7. Common Angles and Exact Trigonometric Values

8. Reading the Graphs of Sine, Cosine, and Tangent

9. Using Identities to Simplify Trigonometric Expressions

10. Modeling Heights, Distances, and Repeating Change

1. Measuring Angles in Degrees

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Why does a full turn have \(360^\circ\)?

Can an angle have a negative degree measure?

Vertex:

Degree:

Acute angle:

Standard position:

Vertex:

Degree:

Acute angle:

Standard position:

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2. Radians and Degree Conversion

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Why is \(\pi\) radians equal to \(180^\circ\)?

Should answers in radians include a decimal?

Radian:

Conversion factor:

Full revolution:

Arc length:

Radian:

Conversion factor:

Full revolution:

Arc length:

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3. Right Triangles and Trigonometric Ratios

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Why are sine, cosine, and tangent ratios instead of lengths?

Can the hypotenuse ever be the adjacent side?

Hypotenuse:

Opposite side:

Adjacent side:

Similar triangles:

Hypotenuse:

Opposite side:

Adjacent side:

Similar triangles:

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4. Solving Right Triangles with Trigonometry

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When should inverse sine, cosine, or tangent be used?

Why can an angle of elevation model the height of a building?

Inverse tangent:

Angle of elevation:

Angle of depression:

Reference angle:

Inverse tangent:

Angle of elevation:

Angle of depression:

Reference angle:

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5. The Pythagorean Theorem and Special Triangles

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Why is the hypotenuse squared alone on one side of the theorem?

How can special triangles help with trigonometry?

Pythagorean theorem:

45-45-90 triangle:

30-60-90 triangle:

Pythagorean triple:

Pythagorean theorem:

45-45-90 triangle:

30-60-90 triangle:

Pythagorean triple:

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6. The Unit Circle Connects Angles and Coordinates

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Why are radians useful on the unit circle?

Why is tangent undefined at some angles?

Unit circle:

Radian:

Terminal side:

Quadrant:

Unit circle:

Radian:

Terminal side:

Quadrant:

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7. Common Angles and Exact Trigonometric Values

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Do I need a calculator to find values at common angles?

How can I remember which function is negative?

Reference angle:

Exact value:

Special triangles:

Degrees and radians:

Reference angle:

Exact value:

Special triangles:

Degrees and radians:

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8. Reading the Graphs of Sine, Cosine, and Tangent

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Why does tangent have breaks in its graph?

What does a negative amplitude do?

Amplitude:

Period:

Midline:

Vertical asymptote:

Amplitude:

Period:

Midline:

Vertical asymptote:

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9. Using Identities to Simplify Trigonometric Expressions

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Why can taking a square root create two possible values?

Is \(\sin^2\theta\) the same as \(\sin(\theta^2)\)?

Identity:

Pythagorean identity:

Reciprocal functions:

Domain:

Identity:

Pythagorean identity:

Reciprocal functions:

Domain:

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10. Modeling Heights, Distances, and Repeating Change

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Should a calculator be in degree or radian mode for a surveying problem?

How do maximum and minimum values determine a sinusoidal model?

Angle of elevation:

Angle of depression:

Periodic model:

Midline value:

Angle of elevation:

Angle of depression:

Periodic model:

Midline value:

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