Understanding Trigonometry in Algebra
Trigonometry studies the relationships between the angles and sides of triangles. It is widely used in algebra, geometry, and calculus.
Basic Trigonometric Ratios
- Sine: \( \sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} \)
- Cosine: \( \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}} \)
- Tangent: \( \tan \theta = \frac{\text{opposite}}{\text{adjacent}} \)
Trigonometric Ratios of Common Angles
Trigonometric Identities
- \( \sin^2 \theta + \cos^2 \theta = 1 \)
- \( 1 + \tan^2 \theta = \sec^2 \theta \)
Graphs of Trigonometric Functions
The graphs of sine, cosine, and tangent functions are periodic and have specific amplitudes and periods.
Applications
Trigonometry is used in physics, engineering, and geometry to solve problems involving angles and distances.
Practice Problems
- Find \( \sin 30^\circ \), \( \cos 60^\circ \), and \( \tan 45^\circ \).
- Solve for \( x \): \( \sin x = 0.5 \).
- Prove \( \tan^2 x + 1 = \sec^2 x \).
📋
Contents
↑