evaluate the following
1. (sin 45 + sin 90) =
2. (cos 30 + cos 60 ) =
3. (sin 60 - sin 90 ) =
4. (Tan 45 + Tan 60 ) =
5. ( Cos 30 - Cos 60
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evaluate the following
1. (sin 45 + sin 90) =
2. (cos 30 + cos 60 ) =
3. (sin 60 - sin 90 ) =
4. (Tan 45 + Tan 60 ) =
5. ( Cos 30 - Cos 60
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Answer:
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
1 : √3 : 2
30-60-90 triangle
From the triangle we get the ratios as follows:
sin cos tan 30, 60
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
sin cos tan 45
Combining the two tables we get:
sin cos tan 30, 45, 60 table