how to find the value of any standard angle ??? for example sin 60*??? without using table
make yourself a sketch of the
30-60-90 ° and the 45-45-90 ° right angled triangles
the ratios of those sides are (in the same order)
1--√3--2 and 1--1--√2
so
sin30 = 1/2 --- csc30 = 2
cos30 = √3/2 --- sec30 = 2/√3
tan30 = 1/√3 ----cot 30 = √3
etc
you have to know the definition of the trig ratios in terms of their names of sides
e.g cos Ø = adjacent/hypotenuse
To find the value of a standard angle like sin 60° without using a table, you can use the unit circle and the properties of right-angled triangles. Here's how you can do it:
1. Start by drawing a unit circle, which is a circle with a radius of 1 unit.
2. Mark the angle you are interested in, in this case, 60°. Place the angle in the standard position, where the initial side lies along the positive x-axis and the terminal side is drawn in the counterclockwise direction.
3. Now, draw a vertical line from the point where the terminal side intersects the unit circle to the x-axis, forming a right-angled triangle.
4. Since the radius of the unit circle is 1, the vertical line you just drew will have a length of sin 60° or the y-coordinate of the point.
5. In a 30-60-90 right triangle, the lengths of the sides are in the ratio 1:√3:2. In this case, the opposite side (vertical line) is the one with length sin 60°, and the hypotenuse is 1.
6. Using the ratio 1:√3:2, we can find the length of the opposite side (sin 60°):
sin 60° = (opposite side) / (hypotenuse) = (√3) / 2.
Therefore, sin 60° is equal to (√3) / 2, which is approximately 0.866.
By following these steps, you can find the value of any standard angle without using a table.