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# 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.

**Explanation**:

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.

### Thus, to find the exact value of trig functions without a unit circle we need to check the quadrant in which the angle falls

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