Trigonometry Rules Page
This page has trigonometry rules, with sin, cos and tan triangle formulas, and problems for the exam.
Trigonometry is included on the advanced algebra and functions part of the Next Generation examination.
Trigonometry Problems
Instructions: Answer the questions about angle a in the right triangle below. The hypotenuse is Y units in length. The other two sides are x and z units in length.
You may wish to refer to the trigonometry formulas, especially the sin, cos and tan triangle formulas below, before answering the questions.
1) tan a = ?
2) cos a = ?
3) sin2 a = ?
4) cos2 a =?
5) sin2 a + cos2 a = ?
Answers to the Trigonometry Problems
1) opposite/adjacent = Z/X
2) adjacent/hypotenuse = X/Y
3) (opposite/hypotenuse)2 = (Z/Y)2
4) (adjacent/hypotenuse)2 = (X/Y)2
5) sin2 a + cos2 a is always equal to 1.
Trigonometry Rules & Formulas:
Memorize the following trigonometry rules and formulas for your exam.
Sin, Cos & Tan – Triangle Formulas
You will need to understand sin, cos, and tan triangle formulas for your exam.
Remember that the hypotenuse is the side of the triangle opposite the right angle.
The adjacent side is next to the angle being measured.
The opposite side is across from the angle that is being measured.
So our sin, cos and tan triangle formulas are as follows:
$latex \text{cosine = } \dfrac{adjacent}{hypotenuse}$
$latex \text{sine = } \dfrac{opposite}{hypotenuse}$
$latex \text{tangent = } \dfrac{opposite}{adjacent}$
Sin, Cos & Tan – Triangle Laws
You will also be asked questions about trigonometric relationships on the examination.
Be sure that you know the key trigonometry rules and formulas.
These are the trigonometry rules relating to the sin, cos, and tan formulas for right triangles:
cos2 A + sin2 A = 1
cos2 A = 1 − sin2 A
sin2 A = 1 − cos2 A
tangent = sin ÷ cos
Trigonometry Rules for Radians
These are the trigonometry rules for radians.
You can think of a radian as a partial circumference of a circle.
θ = s ÷ r [where θ = the radians of the subtended angle; s = arc length; and r = radius]
π × 2 × radians = 360°
π × radians = 180°
π ÷ 2 × radians = 90°
π ÷ 4 × radians = 45°
π ÷ 6 × radians = 30°
More Sin, Cos and Tan (Triangle Formula) Exercises
Free Online Advanced Math Test
Get 400 Extra Accuplacer Math Problems – PDF
Advanced math and trigonometry rules, including sin, cos and tan triangle formulas, are covered in more depth in our free online test.
