TRIGONOMETRY: EVALUATING ANGLES

We will first look into the trigonometric functions of the angles 30˚, 45˚ and 60˚.

Let us consider 30˚ and 60˚.

These two angles form a 30˚-60˚-90˚ right triangle as shown.

The ratio of the sides of the triangle is

From the triangle we get the ratios as follows:

Next, we consider the 45˚ angle that forms a 45˚-45˚-90˚ right triangle as shown. The ratio of the sides of the triangle is

Combining the two tables we get:

Example:

Evaluate the following without using a calculator:

a) 2 sin 30˚ + 3 cos 60˚ – 3 tan 45˚

b) 3(cos 30˚)² + 2 (sin 30˚ )²

Solution:

a) 2 sin 30˚ + 3 cos 60˚ – 3 tan 45˚

b) 3(cos 30˚)² + 2 (sin 30˚)²

EVALUATING OTHER TRIGONOMETRY ANGLES

We could make use of a scientific calculator to obtain the trigonometric value of an angle. (Your calculator may work in a slightly different way. Please check your manual)

Example:

Find the value of cos 6.35˚.

Solution:

Press

cos 6.35˚ = 0.9939 (correct to 4 decimal places)

Example:

Find the value of sin 40˚ 32 ’ .

Solution:

sin 40˚32 ’ = 0.6499 (correct to 4 decimal places)

Example:

Find the value of x for the following triangle. (Give your answer correct to 4 decimal places)

Solution:

x = 6.21 × sin 31.3˚ = 3.2262

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