Give me all answers to speical angles quick check
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How come youve done it multiple times then??
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Sure! To find the special angles, we need to start with some basic angles and use trigonometric ratios. The special angles are those whose trigonometric ratios have exact values and help us simplify calculations.
The following are the special angles in trigonometry:
1. 0 degrees (or 0 radians): This angle lies on the positive x-axis. The trigonometric ratios for this angle are:
- sin(0) = 0
- cos(0) = 1
- tan(0) = 0
2. 30 degrees (or π/6 radians): This angle is formed by rotating 30 degrees in the counter-clockwise direction from the positive x-axis. The trigonometric ratios for this angle are:
- sin(30) = 1/2
- cos(30) = √3/2
- tan(30) = 1/√3
3. 45 degrees (or π/4 radians): This angle is formed by rotating 45 degrees in the counter-clockwise direction from the positive x-axis. The trigonometric ratios for this angle are:
- sin(45) = √2/2
- cos(45) = √2/2
- tan(45) = 1
4. 60 degrees (or π/3 radians): This angle is formed by rotating 60 degrees in the counter-clockwise direction from the positive x-axis. The trigonometric ratios for this angle are:
- sin(60) = √3/2
- cos(60) = 1/2
- tan(60) = √3
5. 90 degrees (or π/2 radians): This angle lies on the positive y-axis. The trigonometric ratios for this angle are:
- sin(90) = 1
- cos(90) = 0
- tan(90) = undefined (division by zero)
These special angles are important in trigonometry as they help us quickly evaluate trigonometric functions without using a calculator. Remembering their exact values can come in handy while solving various mathematical problems.