Find the Other Trig Values in Quadrant III sec(theta)=- square root of 5

Find the Other Trig Values in Quadrant III sec(theta)=- square root of 5
Use the definition of secant to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.
Find the opposite side of the unit circle triangle. Since the adjacent side and hypotenuse are known, use the Pythagorean theorem to find the remaining side.
Replace the known values in the equation.
Negate .
Opposite
Rewrite as .
Use to rewrite as .
Opposite
Apply the power rule and multiply exponents, .
Opposite
Combine and .
Opposite
Cancel the common factor of .
Cancel the common factor.
Opposite
Rewrite the expression.
Opposite
Opposite
Evaluate the exponent.
Opposite
Opposite
Multiply by by adding the exponents.
Multiply by .
Raise to the power of .
Opposite
Use the power rule to combine exponents.
Opposite
Opposite
Opposite
Opposite
Raise to the power of .
Opposite
Subtract from .
Opposite
Rewrite as .
Opposite
Pull terms out from under the radical, assuming positive real numbers.
Opposite
Multiply by .
Opposite
Opposite
Find the value of sine.
Use the definition of sine 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 .
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.
Find the value of cosine.
Use the definition of cosine 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 .
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.
Find the value of tangent.
Use the definition of tangent to find the value of .
Substitute in the known values.
Divide by .
Find the value of cotangent.
Use the definition of cotangent to find the value of .
Substitute in the known values.
Dividing two negative values results in a positive value.
Find the value of cosecant.
Use the definition of cosecant to find the value of .
Substitute in the known values.
Move the negative in front of the fraction.
This is the solution to each trig value.
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Name

Name one billion four hundred seventy-four million six hundred seventy-seven thousand five hundred eighteen

Interesting facts

• 1474677518 has 16 divisors, whose sum is 2281297920
• The reverse of 1474677518 is 8157764741
• Previous prime number is 127

Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 50
• Digital Root 5

Name

Name nine hundred eleven million nine hundred sixty-one thousand nine hundred eighteen

Interesting facts

• 911961918 has 32 divisors, whose sum is 1741132800
• The reverse of 911961918 is 819169119
• Previous prime number is 439

Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 45
• Digital Root 9

Name

Name one billion two hundred eighty-one million nine hundred forty-four thousand six hundred thirty-two

Interesting facts

• 1281944632 has 32 divisors, whose sum is 4349220480
• The reverse of 1281944632 is 2364491821
• Previous prime number is 191

Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 40
• Digital Root 4