Pre-Calculus › Trigonometric Functions
Find the length of an arc of a circle if the radius is and the angle is
radians.
Write the formula to find the arc length given the angle in radians.
Substitute the radius and angle.
Convert to radians.
To convert from degrees to radians, you must multiply by :
. Then, multiply across as you do normally with fractions. Try and simplify if you can. In this case, 60 goes into both 660 and 180.
Thus, your answer is .
Determine the value of in radians.
To convert from degrees to radians, you do:
Find the exact value of each expression below without the aid of a calculator.
In order to find the exact value of we can use the half angle formula for sin, which is
.
This way we can plug in a value for alpha for which we know the exact value. is equal to
divided by two, and so we can plug in
for the alpha above.
The cosine of is
.
Therefore our final answer becomes,
.
Which of the following is equivalent to the expression:
Which of the following is equivalent to the following expression?
Recall our Pythagorean trig identity:
It can be rearranged to look just like our numerator:
So go ahead and change our original expression to:
Then recall the definition of cosecant:
So our original expression can be rewritten as:
So our answer is:
Convert to radians.
To convert from degrees to radians, you must multiply by :
. Then, multiply across as you do normally with fractions. Try and simplify if you can. In this case, 60 goes into both 660 and 180.
Thus, your answer is .
Find the length of an arc of a circle if the radius is and the angle is
radians.
Write the formula to find the arc length given the angle in radians.
Substitute the radius and angle.
Convert to radians.
To convert from degrees to radians, you must multiply by :
. Then, multiply across as you do normally with fractions. Try and simplify if you can. In this case, 60 goes into both 660 and 180.
Thus, your answer is .
Determine the value of in radians.
To convert from degrees to radians, you do:
Simplify .
Write the Pythagorean Identity.
Reorganize the left side of this equation so that it matches the form:
Subtract cosine squared theta on both sides.
Multiply both sides by 3.