Solving Trigonometric Equations By Finding All Solutions  Summary and Q&A
TL;DR
Learn how to find all solutions to trigonometric equations using reference angles and the unit circle.
Key Insights
 ❓ Sine is positive in quadrants one and two, while cosine is positive in quadrants one and four.
 👨💼 Quadrants two and three yield negative values for both sine and cosine.
 ❎ Tangent is negative in quadrants two and four, and positive in quadrants one and three.
 ➕ The square root of a positive value is always positive, hence the plus or minus sign is required.
 🖐️ Reference angles play a crucial role in finding solutions to trigonometric equations, especially when the function is positive or negative in specific quadrants.
 🧡 The period of trigonometric functions determines the range of solutions and helps identify equivalent angles.
 😑 Expressing solutions with the addition of 2πn or πn allows for writing a general equation that encompasses all possible solutions.
Transcript
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Questions & Answers
Q: How do you find the reference angle in trigonometric equations?
The reference angle is found by using the unit circle or the 306090 triangle to determine the angle that corresponds to the given trigonometric value.
Q: What is the period of sine and cosine?
The period of sine and cosine functions is 2π, which means the function repeats every 2π radians or 360 degrees.
Q: How is the period of tangent and cotangent different from sine and cosine?
The period of tangent and cotangent functions is π, which means the function repeats every π radians or 180 degrees.
Q: How should solutions to trigonometric equations be expressed?
To represent all solutions, add 2πn or πn to the reference angle, where n is any integer. This accounts for the periodic nature of trigonometric functions.
Summary & Key Takeaways

Trigonometric equations can be solved by finding the reference angle and adjusting it based on the quadrant where the function is positive or negative.

The period of sine and cosine is 2π, while the period of tangent and cotangent is π.

To find all solutions, add 2πn or πn to the reference angle, where n is any integer.