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Trigonometry

Special Angles

The trigonometric ratios of the angles 30º, 45º and 60º are often used in mechanics and other branches of mathematics. So it is useful to calculate them and know their values by heart.

45º

In this case, the triangle is isosceles. Hence the opposite side and adjacent sides are equal, say 1 unit.
The hypotenuse is therefore of length units (by Pythagoras Theorem).

We have

60º & 30º

Let us draw an equilateral triangle, ABC, of sides 2 units in length. Next draw a line AD from A perpendicular to BC. AD bisects BC giving BD = CD = 1.

From this we can determine the following trig ratios for the special angles 30º and 60º:

General Angles

For any other angle θ, you can calculate approximately the values of sin θ, cos θ, tan θ by using a scientific calculator.

Make sure you set the mode on your calculator to DEG if the angle is measured in degrees or RAD if the angle is measured in radians.

Exercise 2A

Use a calculator to compute the values of the trig functions at the given θ, where θ is measured in degrees.

(Round your answer to 2 decimal places)

θ = º
sin θ = 2 d.p.	cos θ = 2 d.p.	tan θ = 2 d.p.
csc θ = 2 d.p.	sec θ = 2 d.p.	cot θ = 2 d.p.

Exercise 2B

Use a calculator to compute the values of the trig functions at the given θ, where θ is measured in radians.

(Round your answer to 2 decimal places)

θ = radians
sin θ = 2 d.p.	cos θ = 2 d.p.	tan θ = 2 d.p.
csc θ = 2 d.p.	sec θ = 2 d.p.	cot θ = 2 d.p.

Next - Inverse Trigonometric Functions