Trigonometry Fundamentals

10 Questions

What is the measure of a straight angle?

180°

What is the reciprocal of the sine function?

Cosecant

What is the formula for the tangent of the sum of two angles?

(tan(A) + tan(B)) / (1 - tan(A)tan(B))

What is the Pythagorean identity in trigonometry?

sin^2(A) + cos^2(A) = 1

What is the law of cosines used for?

Solving oblique triangles

What is the amplitude of a trigonometric function?

The maximum value of the function

What is the arctan function used for?

Solving equations involving trig functions

What is the formula for the cosine of the sum of two angles?

cos(A)cos(B) - sin(A)sin(B)

What is the difference between an acute angle and an obtuse angle?

An acute angle is less than 90°, while an obtuse angle is greater than 90°

What is the formula for the law of sines?

a / sin(A) = b / sin(B) = c / sin(C)

Study Notes

Angles and Triangles

Angles:
- Measured in degrees, radians, or revolutions
- Can be acute (less than 90°), right (90°), obtuse (greater than 90°), or straight (180°)
Triangles:
- Right triangles have one right angle (90°)
- Oblique triangles have no right angles

Trigonometric Ratios

Sine (sin):
- Opposite side / Hypotenuse
- sin(A) = opposite side / hypotenuse
Cosine (cos):
- Adjacent side / Hypotenuse
- cos(A) = adjacent side / hypotenuse
Tangent (tan):
- Opposite side / Adjacent side
- tan(A) = opposite side / adjacent side
Cotangent (cot):
- Adjacent side / Opposite side
- cot(A) = adjacent side / opposite side
Secant (sec):
- Hypotenuse / Adjacent side
- sec(A) = hypotenuse / adjacent side
Cosecant (csc):
- Hypotenuse / Opposite side
- csc(A) = hypotenuse / opposite side

Trigonometric Identities

Pythagorean Identity:
- sin^2(A) + cos^2(A) = 1
Sum and Difference Formulas:
- sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
- cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
- tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

Solving Triangles

Right Triangle Trigonometry:
- Use trigonometric ratios to find missing sides or angles
Oblique Triangle Trigonometry:
- Use law of sines and law of cosines to find missing sides or angles
Law of Sines:
- a / sin(A) = b / sin(B) = c / sin(C)
Law of Cosines:
- a^2 = b^2 + c^2 - 2bc * cos(A)

Graphs and Inverse Trigonometric Functions

Graphs of Trigonometric Functions:
- Sine, cosine, and tangent functions have periodic graphs
- Amplitude, period, and phase shift can be modified
Inverse Trigonometric Functions:
- arcsin, arccos, and arctan return angles in radians
- Used to solve equations involving trigonometric functions