DETERMINE THE EXACT VALUE OF TRIG FUNCTIONS IN RADIANS

Here we see how to evaluate trigonometric function for the given angle measure using special angles like 0, 30, 45, 60 and 90.

Check the given angle lies in which quadrant.

Step 1 :

Using the concept of reference angle, we can evaluate it easily.

If the given angle lies in the the following quadrants, reference angle can be found like following.

Step 2 :

After using the reference angle, we can make the angles smaller and it will lie in between 0 to 90.

Step 3 :

Using ASTC, we can fix the sign.

Find the exact value of each trigonometric function

Problem 1 :

Solution :

Here 4π/3 is greater than 3π/3 which is π. Then 4π/3 lies in the 3^rd quadrant.

Problem 2 :

Solution :

Here 11π/6 is lesser than 12π/6 which is 2π. Then it will lie in the 4th quadrant. Using reference angle formula and ASTC formula, we get

Problem 3 :

Solution :

Problem 4 :

Solution :

Problem 5 :

Solution :

Evaluating sin (8π/3) :

Evaluating cos (23π/6) :

Evaluating cos (13π/3) :

Evaluating sin (35π/6) :

Applying these values in the given expression.

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