Find the Trig Value csc(theta)=5 with pi/2<theta<pi

Find the Trig Value csc(theta)=5 with pi/2<theta<pi
with
Use the definition of cosecant to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.
Find the adjacent side of the unit circle triangle. Since the hypotenuse and opposite sides are known, use the Pythagorean theorem to find the remaining side.
Replace the known values in the equation.
Negate .
Raise to the power of .
One to any power is one.
Multiply by .
Subtract from .
Rewrite as .
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Multiply by .
Find the value of sine.
Use the definition of sine to find the value of .
Substitute in the known values.
Find the value of cosine.
Use the definition of cosine to find the value of .
Substitute in the known values.
Move the negative in front of the fraction.
Find the value of tangent.
Use the definition of tangent to find the value of .
Substitute in the known values.
Simplify the value of .
Move the negative in front of the fraction.
Multiply by .
Combine and simplify the denominator.
Multiply and .
Move .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
Multiply by .
Find the value of cotangent.
Use the definition of cotangent to find the value of .
Substitute in the known values.
Divide by .
Find the value of secant.
Use the definition of secant to find the value of .
Substitute in the known values.
Simplify the value of .
Move the negative in front of the fraction.
Multiply by .
Combine and simplify the denominator.
Multiply and .
Move .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
Multiply by .
This is the solution to each trig value.
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Name

Name one billion nine hundred five million nine hundred thirteen thousand five hundred ninety-two

Interesting facts

• 1905913592 has 64 divisors, whose sum is 7655160960
• The reverse of 1905913592 is 2953195091
• Previous prime number is 11

Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 44
• Digital Root 8

Name

Name one billion four hundred sixty million four hundred thirty-seven thousand nine hundred seventeen

Interesting facts

• 1460437917 has 32 divisors, whose sum is 2035608960
• The reverse of 1460437917 is 7197340641
• Previous prime number is 97

Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 42
• Digital Root 6

Name

Name one billion four hundred fifty-four million one hundred thirty-one thousand eight hundred

Interesting facts

• 1454131800 has 256 divisors, whose sum is 6711828480
• The reverse of 1454131800 is 0081314541
• Previous prime number is 271

Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 27
• Digital Root 9