Question

Given cot A= 11/60 and that angle A is in Quadrant I, find the exact value of cos cos A in simplest radical form using a rational denominator.

Answer 1

Answer: Below

Step-by-step explanation:cotA=11/60

tan=opposite/adjacent

cot=1/tan

cot=adjacent/opposite

cotA=11/60

adjacent=11

opposite=60

using the Pythagorean Theorem, the hypotenuse=61

csc=1/sin

cscA=1/sinA

sin=opposite/hypotenuse

sinA=60/61

csc=1/sin

cscA=61/60

Answer 2

The value of Cos A is $\frac{11}{61}$.

What is cosine of an angle?

The cosine of an angle is defined as the sine of the complementary angle. The complementary angle equals the given angle subtracted from a right angle, 90°. For instance, if the angle is 30°, then its complement is 60°.

According to the given problem,

Given, cot A = $\frac{11}{60}$,  and angle A is in first quadrant then, all the function's value will be positive in nature.

Now, cot A = $\frac{Base}{Perpendicular}$

cot A =  $\frac{11}{60}$

Base = 11

Perpendicular = 60  

Using the Pythagorean Theorem

Hypotenuse² =  Perpendicular² +Base²

⇒ Hypotenuse² = 11² + 60²

⇒ hypotenuse = 61

Then, Cos A = $\frac{Base}{Hypotenuse}$

Cos A = $\frac{11}{61}$

Hence, we can conclude that Cos A is $\frac{11}{61}$.

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