x is an acuate. Find the value of x in

Monique Slaughter

Monique Slaughter

Answered question

2021-12-11

x is an acuate. Find the value of x in degrees
cos(x)=33
x=?

Answer & Explanation

Matthew Rodriguez

Matthew Rodriguez

Beginner2021-12-12Added 32 answers

Step 1
Given
cot(x)=33
cot(x)=13
x=cot1(13}
arrwox=60
Edward Patten

Edward Patten

Beginner2021-12-13Added 38 answers

Step 1
Take the inverse cotangent of both sides of the equation to extract x from inside the cotangent.
x=arot(33)
The exact value of arot(33) is π3
x=π3
The cotangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from π to find the solution in the fourth quadrant.
x=π+π3
Simplify π+π3
To write π1 as a fraction with a common denominator, multiply by 33
x=π1×33+π3
Write each expression with a common denominator of 3, by multiplying each by an appropriate factor of 1.
Combine.
x=π×31×3+π3
Multiply 3 by 1
x=π×33+π3
Combine the numerators over the common denominator.
x=π×3+π3
Simplify the numerator.
Move 3 to the left of π
x=3×π+π3
Add 3π and π
x=4π3
Find the period
The period of the function can be calculated using π|b|
Replace b with 1 in the formula for period.
π|1|
Solve the equation.
The absolute value is the distance between a number and zero. The distance between 0 and 1 is 1
π1
Divide π by 1
π
The period of the cot(x) function is π so values will repeat every π radians in both directions
x=π3+πn
4π3+πn
for any integer n
Consolidate the answers.
x=π3+πn for any integer n

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