How to find the exact value of trig functions without a unit circle?
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Answer: To find the exact value of trig functions without a unit circle, we need to check the quadrant in which the angle falls.
Let us proceed step by step.
To find the exact value of trig functions without a unit circle, we need to consider one example to understand it more clearly.
Let's find the value of cos 23π / 6
Step 1- First we need to check that the angle falls in which quadrant.
Step 2 - For one full rotation is 2π which can be written as 12 π / 6
Two complete anti-clockwise rotations starting from the positive X-axis make an angle of 4π.
To check its quadrant, 23 π / 6 = 4 π - π / 6.
Hence, it falls in the fourth quadrant and as we can see from the above figure cos is positive in the fourth quadrant.
So we will calculate cos π/6 = (√3)2
Hence we got the value of cos 23π/6 = (√3)/2 without a unit circle.