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Trigonometry

Converting Trigonometric Values

If the value of one trig function is known, any of the other trig functions can be calculated.

Example

Suppose α = tan θ is known.

This situation can be represented by the following diagram. We set the adjacent side to length 1.  Then using the definition of tangent, the opposite side must have length tan θ, thar is, α.

Using Pythagoras Theorem we find the hypotenuse is of length . Each of the three sides are now determined and

and .

Exercise 4

Suppose α = sin θ is known. Find tan θ and cos θ in terms of α.

Answer

Exercise 5

Suppose α = cos θ is known. Find tan θ and sin θ in terms of α.

Answer