# Find the Other Trig Values in Quadrant III sec(theta)=- square root of 2

Find the Other Trig Values in Quadrant III sec(theta)=- square root of 2
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
Any root of is .
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.
Divide by .
Find the value of cosecant.
Use the definition of cosecant to find the value of .
Substitute in the known values.
Simplify the value of .
Move the negative one from the denominator of .
Rewrite as .
This is the solution to each trig value.
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### Name

Name one billion three hundred twenty million twenty-one thousand eight hundred twenty-eight

### Interesting facts

• 1320021828 has 32 divisors, whose sum is 3330340200
• The reverse of 1320021828 is 8281200231
• Previous prime number is 109

### Basic properties

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

### Name

Name one billion one hundred four million one hundred forty-three thousand seven hundred five

### Interesting facts

• 1104143705 has 16 divisors, whose sum is 1730576640
• The reverse of 1104143705 is 5073414011
• Previous prime number is 7

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 26
• Digital Root 8

### Name

Name one billion seven hundred thirty-six million four hundred sixty thousand three hundred fifty-five

### Interesting facts

• 1736460355 has 32 divisors, whose sum is 2438553600
• The reverse of 1736460355 is 5530646371
• Previous prime number is 449

### Basic properties

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