Trigonometric Functions (Cambridge (CIE) IGCSE Additional Maths) : Revision Note

Trigonometric Functions

What are the trigonometric functions?

• The three standard trigonometric functions are: sine, cosine and tangent

• The functions are many-to-one mappings

  • They do not have inverses unless their domain is restricted

How can I use the trigonometric functions with right-angled triangles?

• The three trigonometric functions sine, cosine and tangent give the ratios of side lengths in right-angled triangles

• For an acute angle in a right-angled triangle:

  • Sine of the angle is the length of the side opposite the angle divided by the hypotenuse

  • Cosine of the angle is the length of the side adjacent to the angle divided by the hypotenuse

  • Tangent of the angle is the length of the opposite side divided by the length of the adjacent side

• You can use the acronym SOHCAHTOA to help you remember these

How can I use the trigonometric functions with non-right-angled triangles?

• You can find missing angles and the lengths of missing sides using the sine rule and the cosine rule

• You can also use the area formula

Reciprocal Trig Functions

What are the reciprocal trig functions?

• There are three reciprocal trig functions that each correspond to either sin, cos or tan

  • Secant (sec x)

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  • Cosecant (cosec x)

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  • Cotangent (cot x)

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• A good way to remember which function is which is to look at the third letter in each of the reciprocal trig functions

  • cot x is 1 over tan x etc

• Each of the reciprocal trig functions are undefined for certain values of x

  • sec x is undefined for values of x for which cos x = 0

  • cosec x is undefined for values of x for which sin x = 0

  • cot x is undefined for values of x for which tan x = 0

    • When tan x is undefined, cot x = 0

• Be careful not to confuse the reciprocal trig functions with the inverse trig functions

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