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Introduction to Trigonometry

Understand the unit circle, radian measure, and graphs of trigonometric functions.

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Introduction to Trigonometry

Radian Measure

Radians=Degrees×π180\text{Radians} = \text{Degrees} \times \frac{\pi}{180}

DegreesRadians
0°0°00
30°30°π6\frac{\pi}{6}
45°45°π4\frac{\pi}{4}
60°60°π3\frac{\pi}{3}
90°90°π2\frac{\pi}{2}
180°180°π\pi
360°360°2π2\pi

The Unit Circle

A circle with radius 1 centered at the origin. For angle θ\theta: cos⁡θ=x-coordinatesin⁡θ=y-coordinate\cos \theta = x\text{-coordinate} \quad \sin \theta = y\text{-coordinate}

Key Values

θ\thetasin⁡θ\sin \thetacos⁡θ\cos \thetatan⁡θ\tan \theta
00001100
π6\frac{\pi}{6}12\frac{1}{2}32\frac{\sqrt{3}}{2}33\frac{\sqrt{3}}{3}
π4\frac{\pi}{4}22\frac{\sqrt{2}}{2}22\frac{\sqrt{2}}{2}11
π3\frac{\pi}{3}32\frac{\sqrt{3}}{2}12\frac{1}{2}3\sqrt{3}
π2\frac{\pi}{2}1100undefined

Graphing Trig Functions

y=Asin⁡(Bx−C)+Dy = A\sin(Bx - C) + D

  • Amplitude: ∣A∣|A|
  • Period: 2π∣B∣\frac{2\pi}{|B|}
  • Phase shift: CB\frac{C}{B}
  • Vertical shift: DD

Sine: Starts at 0, goes up

Cosine: Starts at max, goes down

Tangent: Has vertical asymptotes, period π\pi

Identities to Know

Pythagorean Identity

sin⁡2θ+cos⁡2θ=1\sin^2 \theta + \cos^2 \theta = 1

Reciprocal Functions

csc⁡θ=1sin⁡θ,sec⁡θ=1cos⁡θ,cot⁡θ=1tan⁡θ\csc \theta = \frac{1}{\sin \theta}, \quad \sec \theta = \frac{1}{\cos \theta}, \quad \cot \theta = \frac{1}{\tan \theta}

Memory for signs: "All Students Take Calculus" — tells which trig functions are positive in quadrants I, II, III, IV.

Explain using:

⚠️ Common Mistakes: Introduction to Trigonometry

Avoid these 3 frequent errors

🌍 Real-World Applications: Introduction to Trigonometry

See how this math is used in the real world

📝 Worked Example: Solving a Quadratic by Factoring

Problem:

Solve x2−5x+6=0x^2 - 5x + 6 = 0.

2Factor the quadratic
3Set each factor equal to zero
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❓ Frequently Asked Questions

What is Introduction to Trigonometry?▾
Understand the unit circle, radian measure, and graphs of trigonometric functions.
How can I study Introduction to Trigonometry effectively?▾
Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Regular review and active practice are key to retention.
Is this Introduction to Trigonometry study guide free?▾
Yes — all study notes, flashcards, and practice problems for Introduction to Trigonometry on Study Mondo are free to access. No account is needed.
What course covers Introduction to Trigonometry?▾
Introduction to Trigonometry is part of the Algebra 2 course on Study Mondo, specifically in the Trigonometric Functions section. You can explore the full course for more related topics and practice resources.