# Trig Problems

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For any given angle, we can apply trigonometric functions such as sine, cosine, tangent, cosecant, secant and cotangent to get the measure of it. These trigonometric functions help us calculate the measure of the sides and angles in triangles and other geometric shapes. In trigonometry, given an angle, we can convert the angle from degrees to radians and vice-versa and these angles and functions are used in real-world to calculate the distance between any two objects or heights of buildings etc.

Example 1: Given an angle ‘x’ in the first quadrant of the coordinate plane. If sin(x) = 2/√13, then what is the value of cos(x)?

Given: sin(x) = 2/√13.

According to the trigonometric identity: sin2(x) + cos2(x) = 1.

This gives: cos2(x) = 1 – sin2(x)

Applying the above formula we get -> cos2(x) = 1 – (2/√13)2

This gives: cos2(x) = 1 – 4/13

Taking the common denominator we get: cos2(x) = (13 – 4)/ 13 = 9/13

Hence, cos(x) = √(9/13) = 3/√13.

Therefore the value of cos(x) = 3/√13.

Example 2: Given an angle ‘x’ in the first quadrant of the coordinate plane. If cos(x) = 9/15, then what is the value of sin(x)?

Given: cos(x) = 9/15.

According to the trigonometric identity: sin2(x) + cos2(x) = 1.

This gives: sin2(x) = 1 – cos2(x)

Applying the above formula we get -> sin2(x) = 1 – (9/15)2

This gives: sin2(x) = 1 – 81/225

Taking the common denominator we get: sin2(x) = (225 - 81)/ 225 = 144/225.

Hence, sin(x) = √(144/225) = 12/15

Therefore the value of sin(x) = 12/15.