Trigonometry and Geometry Concepts (Flashcards)

Vocabulary flashcards covering key trig and geometry concepts from the lecture notes.

What is the Pythagorean theorem relating legs a, b and hypotenuse c of a right triangle?

a^2 + b^2 = c^2

What characteristic defines similar triangles in terms of their side ratios?

If \triangle ABC is similar to \triangle DEF (\triangle ABC \sim \triangle DEF), then the ratios of corresponding sides are equal: \frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD}

In a right triangle with legs a and b, and hypotenuse c, which side is opposite the right angle and typically the longest?

The hypotenuse, c

In a right triangle for angle \theta, which side is directly across from \theta?

The opposite side

In a right triangle for angle \theta, which side is next to \theta but not the hypotenuse?

The adjacent side

What is the trigonometric ratio for sine of angle \theta?

\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}

What is the trigonometric ratio for cosine of angle \theta?

\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}

What is the trigonometric ratio for tangent of angle \theta?

\tan \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{\sin \theta}{\cos \theta}

What is the reciprocal identity for secant of angle \theta?

\sec \theta = \frac{1}{\cos \theta}

What are the coordinates (x, y) of a point on the unit circle at angle \theta?

(x, y) = (\cos \theta, \sin \theta)

What equation defines a Pythagorean Triplet (a, b, c)?

a^2 + b^2 = c^2

What is the formula for the area (A) of a right triangle with legs a and b?

A = \frac{1}{2}ab

In a 45-45-90 right triangle, if a leg has length x, what is the length of the hypotenuse?

x\sqrt{2}

In a 30-60-90 right triangle, if the shortest leg is x, what is the length of the hypotenuse?

2x

What is the reciprocal identity for cosecant of angle \theta?

\csc \theta = \frac{1}{\sin \theta}

What is the reciprocal identity for cotangent of angle \theta?

\cot \theta = \frac{1}{\tan \theta}

If \sin \theta = x, solve for \theta using the inverse sine function.

\theta = \arcsin(x)

If \cos \theta = x, solve for \theta using the inverse cosine function.

\theta = \arccos(x)

If \tan \theta = x, solve for \theta using the inverse tangent function.

\theta = \arctan(x)

State the Law of Sines for a triangle with angles A, B, C and opposite sides a, b, c.

\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}