Made by: Wasim
Trigonometric Functions
Table of Contents
• About
• Formulas
• Identities
• Values
• Quadrants
• Graphs
• Domain & Range
• Key Terms
Trigonometric Functions
• Trigonometric functions are the functions of an angle of a triangle. Ergo, the relationship
between the angles and sides of a triangle are given by these functions.
• The six basic trigonometric functions:
• Sine
• Cosine
• Tangent
• Cosecant
• Secant
• Cotangent
Formulas
Trigonometric Functions
• The basic formulas to find the trigonometric functions are as follows:
• sin 𝜃 =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
• cos 𝜃 =
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
• tan 𝜃 =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡
• cosec 𝜃 =
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒
• sec 𝜃 =
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡
• cot 𝜃 =
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒
Identities
Trigonometric Functions
Reciprocal Identities
• cosec θ =
• sec θ =
• cot θ =
1
sin θ
1
cos θ
1
tan θ
Quotient Identities
• tan θ =
• cot θ
sin θ
cos θ
cos θ
=
sin θ
Pythagorean Identities
Sum & Difference Identities
• cos 2 x + sin2 x = 1
• 𝑠𝑖𝑛 (𝐴 + 𝐵) = 𝑠𝑖𝑛 𝐴 𝑐𝑜𝑠 𝐵 + 𝑐𝑜𝑠 𝐴 𝑠𝑖𝑛 𝐵
• 1 + tan2 x = sec 2 x
• 𝑐𝑜𝑠 (𝐴 + 𝐵) = 𝑐𝑜𝑠 𝐴 𝑐𝑜𝑠 𝐵 − 𝑠𝑖𝑛 𝐴 𝑠𝑖𝑛 𝐵
• cot 2 x + 1 = csc 2 x
• 𝑡𝑎𝑛 (𝐴 + 𝐵) =
𝑡𝑎𝑛 𝐴 + 𝑡𝑎𝑛 𝐵
1 − 𝑡𝑎𝑛𝐴𝑡𝑎𝑛𝐵
• 𝑠𝑖𝑛 (𝐴 − 𝐵) = 𝑠𝑖𝑛 𝐴 𝑐𝑜𝑠 𝐵 − 𝑐𝑜𝑠 𝐴 𝑠𝑖𝑛 𝐵
Double-Angle Identities
• sin2A = 2sinAcosA
• cos2A = cos 2 A − sin2 A
• tan2A =
2tanA
1−tan2 A
• 𝑐𝑜𝑠 (𝐴 − 𝐵) = 𝑐𝑜𝑠 𝐴 𝑐𝑜𝑠 𝐵 + 𝑠𝑖𝑛 𝐴 𝑠𝑖𝑛 𝐵
• 𝑡𝑎𝑛 (𝐴 − 𝐵) =
𝑡𝑎𝑛 𝐴 − 𝑡𝑎𝑛 𝐵
1 + 𝑡𝑎𝑛𝐴𝑡𝑎𝑛𝐵
Quadrants
Graphs
Domain
& Range
Key Terms
Trigonometric Functions
• 𝑦 = 𝑎𝑠𝑖𝑛𝑏 𝑥 − 𝑐 + 𝑑
• Amplitude – a – the maximum vertical distance the graph of a sinusoidal function
varies above and below the horizontal central axis of the curve, or else, the y-axis.
•
𝑀𝑎𝑥 −𝑀𝑖𝑛
2
• Period – T – the length of the interval of the domain over which a graph repeats itself,
or in other words, the horizontal length of one cycle on a periodic graph.
•
360
|𝑏|
• Vertical Displacement – d – the vertical translation of the graph of a periodic function.
• Phase Shift – c – the horizontal translation of the graph of a periodic function.
To conclude
The trigonometric functions and identities are the ratio of sides of a rightangled triangle. The sides of a right triangle are the perpendicular side,
hypotenuse, and base, which are used to calculate the sine, cosine, tangent,
secant, cosecant, and cotangent values using trigonometric formulas.
Thank you for paying attention!