TRIGONOMETRY FOR STATICS

PART 3:

Values of Trigonometric Functions at Specific Angles:

For 0^o and 90^o: These functions are limiting values that can be observed from the drawing. As side y approaches 0 (zero), the x approaches r.

For 30^o and 60^o_:

For 45^o_:

Trigonometric Identities:

Basic identities:

Half-angles:

Identities in terms of tan (q/2):

where

Curves of Sine, Cosine, and Tangent:

Sine function:

The sine function is an odd function since

Cosine function:

The cosine function is an even function since

Tangent function:

The tangent function is an odd function since

Note that

as

Approximation of Trigonometric Functions at Small Angles:

As a close approximation, when an angle(expressed in radians) is very small, we may use the following approximations

• replace with
• replace with
• replace with unity (i.e., )

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