to find of trigonometric ratios of angles 60
You should memorize the ratio of sides of the
30-60-90 right-angled triangle
the ratio of sides are 1 : √3 : 2 correspondingly, if you forget where the numbers go, remember the smallest side is across the smallest angle, the largest side across the largest angle, etc.
(notice 1^2 + (√3)^2 = 2^2)
You can now form any trig ration of 30 and 60 degrees.
You should also memorize the 45-45-90 triangle
which has sides in the ration of 1:1:√2
To find the trigonometric ratios of angles, you can use the unit circle or refer to trigonometric tables. Let's explain how to find the trigonometric ratios for an angle of 60 degrees.
The three primary trigonometric ratios for any angle are sine (sin), cosine (cos), and tangent (tan).
1. Sine (sin): To find the sine of an angle, divide the length of the side opposite the angle by the length of the hypotenuse in a right triangle. However, for special angles like 60 degrees, you can directly refer to the trigonometric table or use the values from the unit circle. For 60 degrees, the sine value is 0.866.
2. Cosine (cos): To find the cosine of an angle, divide the length of the adjacent side by the length of the hypotenuse in a right triangle. Again, you can refer to the trigonometric table or use the unit circle. For 60 degrees, the cosine value is 0.5.
3. Tangent (tan): To find the tangent of an angle, divide the length of the side opposite the angle by the length of the adjacent side in a right triangle. Alternatively, you can calculate it by dividing the sine value by the cosine value (tan = sin/cos). For 60 degrees, the tangent value is 1.732.
So, the trigonometric ratios for an angle of 60 degrees are:
- sin(60) = 0.866
- cos(60) = 0.5
- tan(60) = 1.732
Remember that these values are often rounded for convenience, and you can use more precise values if needed.